All religions look like superstition to those who don't believe in the religion. Miracles are only miracles to believers; to the rest they're phenomena, or mere coincidence.

"One man's religion is another man's belly laugh." R.A. Heinlein―Time Enough for Love

Non-religion looks like superstition to the religious too. Indeed, the non-religious are most often blindsided by their irrational belief in their own objectivity.

(Quite weird -- I accidentally hit some key while typing my name and it accepted the comment without any word verification. Can't reproduce it again. Although I notice on several occasions when I just couldn't read the word verification I got away with my best attempt, even though the chances of me having got it right on every such occasion are very low. While I'm on the subject of blog technicalities -- Zeyad, your blog's main page takes forever to load with every post going back to the beginning of last year).

If you ever get a chance, Zeyad, and you enjoy plays, you should see Over the Tavern. It's set in 1950's America and revolves around a young boy and his family. The boy is starting to quesiton some of the things about his religion. It's meaningful and hilarious. :)

While I'm on the subject of blog technicalities -- Zeyad, your blog's main page takes forever to load with every post going back to the beginning of last year).

I noticed that too. But I thought it was just me, or rather my computer. The one at home, which is using XP, is slower than the one at work, which is using Windows 7. I thought it might have to do with my anti-virus software.

"Non-religion looks like superstition to the religious too."

This suggests an inability among the religious to differentiate between agnosticism and atheism. Notwithstanding your assertion above, I suspect this inability isn't universally, or even commonly, shared among those who are religious. Perhaps you're being blinded by an irrational belief in your own perceptivity.

Unfortunately, my parents poisoned my mind with syfy and horror movies from the time when we were in the UK. I only broke free from their spell as a grown up.

"This suggests an inability among the religious to differentiate between agnosticism and atheism."

This suggests you're trying to be a smart arse. The religious tend to be better educated, on the whole, about systems of belief (although that's not saying much, and should be expected anyway, since they have skin in the game).

To cut to the chase, you're wrong. Atheists don't tend to be superstitious, they tend to be deluded dogmatists. They're vastly outnumbered by the superstitious agnostics.

"I noticed that too. But I thought it was just me, or rather my computer. The one at home, which is using XP, is slower than the one at work, which is using Windows 7."

Yes, and IE9 is slower than Firefox on my new i5 laptop. But they're both a lot slower than they should be.

A bait and switch goin’ down there, ‘cept I caught it.

I would not dispute that many agnostics are superstitious to a greater or lesser degree, but that observation is quantitatively different from your assertion that ‘[n]on-religion looks like superstition to the religious." I still think you're projecting your failure to differentiate agnosticism from atheism. (In fact, I'd almost bet you'd be agreeing by now that your initial statement was way overbroad were it anybody but me who'd called ya out on it.)

"A bait and switch goin’ down there, ‘cept I caught it."

Well, didn't take long for this exchange to take a boringly familiar twist.

"that observation is quantitatively different from your assertion that ‘[n]on-religion looks like superstition to the religious.'"

I'm quite aware of that. That latter statement was not made to support my original contention, merely to point out that I distinguish greatly between agnostics and atheists, to the extent that I don't consider the latter to be non-religious at all.

"I still think you're projecting your failure to differentiate agnosticism from atheism. (In fact, I'd almost bet you'd be agreeing by now that your initial statement was way overbroad were it anybody but me who'd called ya out on it.)"

And I still think you're tryin' to be a smart arse. So don't go expectin' any "debate" if y'all wanna engage in yer usual pedantry.

"I don't consider [atheism] to be non-religious at all."

Ah yes, figured you was going there again. The notion that denial of the existance of God and the belief that all religion is either delusion or hoax is a religion of it's own. I remember your assertion from last time.

But, I've run across that one before, usually from Protestant evangelicals, but there is a Catholic version. And I have long recognize that to be a political statement rather than a religious one. Of course, the Protestant evangelicals, and your version of Catholicism are political as well as religious beliefs. Happily, I live in a country where the Constitution keeps folks like you in check.

Rather than wait for Lee to check all that for booby traps, I'll just cut to the chase and observe that he's settin' up to claim a distinction between superstition as an accidental trait of the self-labelled non-religious, and -- as I would claim -- an almost unavoidable consequence of the abandonment of traditional world views which took a rational progressive view of human nature and the natural world.

(And yes, I even include Islam among those world views, being, as I am, increasingly impressed by the medieval Islamic scholars that I'm reading about. I was always aware of their role as a conduit for the arrival of Greek learning in medieval Europe, but I don't think I was quite aware of how advanced and progressive their own science was.

Perhaps it would be better, at least more accurate, to say: ‘I have long recognize that to be a political statement rather than a strictly religious one.”

"The notion that denial of the existance of God and the belief that all religion is either delusion or hoax is a religion of it's own."

Now who's talkin' about bait and switch? Atheism, as I'm sure you well know but I will give you the benefit of the doubt anyway, is more than the denial of the existence of God. It is the positive assertion that the "natural" world is "all there is". You may be able to see that those are different things.

"…Atheism…is more than the denial of the existence of God."

See the word ‘and’ in the phrase ‘…denial of the existance of God and…’ and try to follow along from there. If you're gonna insist on carryin’ on, at least try to keep up.

Perhaps it would be better, at least more accurate, too say: ‘I have long recognize that to be a political statement rather than a strictly religious one.'"

Yes, it would be a great deal better and more accurate to say that. I'm glad you rethought it.

"Of course, the Protestant evangelicals, and your version of Catholicism are political as well as religious beliefs. Happily, I live in a country where the Constitution keeps folks like you in check."

Happily, I live in a country where the US constitution can be read objectively, and not through the lens of overly zealous evangelicals or "liberals". Your constitution says nothing whatever about keeping Protestants, Catholics, or anyone else in check. It grants them the same rights to hold whatever political views they damn well like, same as anyone else. I'll put your misinterpretation of its anti-establishment clauses down to a temporary rattiness borne of yer anti-religious enthuiasm.

"See the word ‘and’ in the phrase ‘…denial of the existance of God and…’ and try to follow along from there. If you're gonna insist on carryin’ on, at least try to keep up."

Didn't want to embarrass you further, but if you insist ....

"... and the belief that all religion is either delusion or hoax is a religion of it's own"

So, by your own words, atheism is a belief. Good. Now keep up here ... do you think it is an evidence-based belief or something else? If the former, what evidence do you think it's based on? (And just to keep you focussed, remember we are talking about a positive assertion here, so don't bother with any namby-pamby retorts about LACK of evidence or balance of probabilities).

"Your constitution says nothing whatever about keeping Protestants, Catholics, or anyone else in check."

No, it does not use that language. But it serves the intended purpose quite nicely nonetheless. There is much to be said for how well written it was. Got a lot done in only three pages.

"I'd have to think that would depend on the atheist. I don't suppose they all come to their conclusions the same way."

I can see you have no intention of answering the question. But I'll try one more time: do you think any atheists' atheism is evidence-based, and what do you suppose that evidence is?

While Lee lets the sniffer dogs loose on that last one, a quick chance for me to remark on the role of Iraq in the history of mathematics, which I've also been reading up on. There's a newish (2008) book that I'd like to read sometime: "Mathematics in Ancient Iraq: A Social History". From the earliest Sumerian scribblings, to the medieval Islamic period, Iraq has been at the centre of things mathematical. And while we've got some papyri from ancient Egypt showing mathematical development there, Babylonian baked clay tablets were much more robust as records and exist today in much greater number. Babylonia probably contributed as much if not more than Egypt to later Hellenistic maths. Some day I'll find more time to read up on it.

"But I'll try one more time: do you think any atheists' atheism is evidence-based, and what do you suppose that evidence is?"

I'm sorry, but it has never occurred to me to delve into the reasons for an atheist's denial of the existance of God (or gods). It never interested me and then there was the overarching logical problem of attempting proof of a negative. In fact, I recall, whilst checking the Heinlein quote for accuracy this morning, that I skimmed across a Google entry that said something about proving that there was no god, something about having 50 proofs, or something like that, and I recall thinking at the time that they obviously needed a lesson in basic logic. But it never occurred to me to examine the web site behind the Google entry.

So, no. I have no intention of answering the question you posed. I don't happen to have an answer handy, and I've never been interested in the subject--still ain't. So, I'm not gonna go lookin’ for one.

"The notion that denial of the existance of God and the belief that all religion is either delusion or hoax is a religion of it's own. I remember your assertion from last time. But, I've run across that one before... [a]nd I have long recognize (sic) that to be a political statement rather than a religious one."

You are now sayin' you don't know jack shit about the topic? Indeed, that you not only don't know but don't care to be informed? Ok, figures. I guess we won't be movin' on to the topic of agnosticism and superstition then.

"You are now sayin' you don't know jack shit about the topic?"

No, not what I'm saying. Rather, anybody who claims to have compelling evidence or actual proof of the negative, i.e. that there is no God (or gods) has obviously made a fundamental logical error; either in the chain of logic, or in the premises. If they happen to be right, it's obviously by accident. So why should I be interested in their claims to evidence or proof? Be like watchin’ Bruno tryin’ to do his occasional elephant jumps. Ain't worth wastin’ time on.

You're obviously willing to argue what you know to be loser of an argument, just for the sake of having the argument. Seen ya do it too many times not to have figured that much out. But, I am not so inclined.

Up to you whether or not you move on to agnostics and superstitions. But, I'm inclined to bet that if you cannot confuse the two classes startin’ out (atheists and agnostics) you'll not want to deal with the second class at all. I figure this whole thing was predicated for you on being able to blur the line and slide a flauwed argument in behind the blurr. If that's not gonna work, you'll be losin’ interest real quick. (You'll go out with a bunch of bluster, of course, but you'll be headin’ out sure ‘nuff.)

Although, you gotta admire his sheer brass neck too, accusing' me of trying' to muddy the waters with an argument HE brought up, and then, after being' too stupid to understand the explication of his own confusion, tryin' to turn the tables. Not many would be so brazen.

Morning has broken, and no further sign of the Catholic theocracy raising it's hoary head again… Perhaps time for a summary, for those who've been trying to follow our little exchange.

The American fundamentalist Christian evangelical (Protestant variety) has been developing an argument in recent years to the effect that our Constitutional right to freedom of religion does not include the right to be free of religion. I.e: Freedom of religion does not include the right to freedom from religion. In service of this fundy political theory they've been trying to promote the argument that secularism, an absence of religion, is properly to be seen as a religion in and of itself. They think this will reduce the claim to a right to be free of government promotion of religion to the status of a competing religion and give them a political advantage they do not currently enjoy in e.g the arguments over whether ‘creationism’ should be taught in science classes in the public schools as a credible alternative to the theory of evolution and stuff like that. Catholic fundies like Petes also see a potential opening for their theocratic agenda if they can sell the idea that secularism is religion. They figure they can reduce the right to be free of religion to the status of a competing religion, and thus ‘level the playing field’ as they see it.

I was not cooperating with Petes in his attempt to re-classify a position of no religious preferences to the status of a competing religion, with no protections not enjoyed by his own religion. In effect, he wants to ‘demote’ secularism to what he feels is the disadvantaged status of a competing religion. There is a political agenda behind this which the reader can probably figure out for themselves at this point. But, I was not cooperating in the required blurring of the lines that's a necessary first step in developing his argument. So he sorta blustered a bit and then seems to have faded away.

More re: American politics: But this time economics, not religion.

"In a speech Tuesday, [John] Boehner (leader of the House Republicans) said that ‘allowing America to default,’ while not such a hot idea, would be better than raising the debt ceiling without ‘dramatic steps to reduce spending.’ Added Boehner: ‘We shouldn’t dread the debt limit. We should welcome it. It’s an action-forcing event in a town that has become infamous for inaction.’" WaPo

Those clowns are gonna do it again; they didn't learn anything from last time.

LMFAO. Only Lee could be egotistical enough to take his own misguided suspicions and suggestion from 2:23 PM above, mix in a few political fantasies and attribute them to me, construct his own monologue based thereon, and declare himself 'the winner'. Lee-world must be such a fun place.

I got plenty 'bout it. Would be happy to expound it too, 'ceptin' I know you are gonna vanish up yer own ass to soliloquise, then emerge back into the light to announce that even though you know jack shit about it you still won the argument you just had with y'all's own self.

No secrets involved. I can see how it would appear so to y'all though, 'cos even though y'all's only interested in debating' with y'all's own self, y'all may still harbour a nigglin' worry about what it is y'all is so desperate to avoid hearing'.

If you had something you thought I was ‘desperate to avoid hearing’ I'd not be able to shut you up on the subject. This is just more of your stock Great and Wonderful Petes stuff, like those mighty mystery maths that you never did get around to unveiling way back when…

LOL. Y'all really have y'all's obfuscatory tactics down to a fine art at this stage. If only there was a way to monetise them in the real world y'all could make a livin' from it instead of trollin' this forum. You sure y'all's not some kind of failed librul politician?

Struck a funny bone, more like. Remember how you refused to multiply out a^2 - b^2 because it proved the factorisation you had been arguin' for was poppycock? That was probably the greatest Lee C classic of all time. Jes' refused to do the sums, no sirree. Wouldn't even agree on what factorisation meant (although I never did find out if y'all was too dumb to know, or, more likely, it didn't suit y'all to know). Laugh a minute. Particularly funny in the light of yer comments here, since y'all proved that the most Jesuitical of Jesuits was alive and well and livin' in the woods of Indiana. Even the ones that wouldn't look thru Galileo's telescope would have blushed for y'all. What a hoot.

This from the guy who promised to show us 'hundreds’ of ways to factor a binomial expression (There are a maximum of four.) And then conspicuously failed to deliver even the four.

This from the guy who promised to show us 'hundreds’ of ways to factor a binomial expression. (There are a maximum of four.) And then conspicuously failed to deliver even the four.

Decided to give up on the factoring and go for simple multiplication did ya? You flush out fairly easy these days. (Although, I must give ya credit for persistence in the continued hunt for a winner. You do keep chasin’ the dream.)

You've already done the telescope bit. You need new material; you're circlin’ back too quick. Ya got too small a circle here; need to expand your field.

(for the audience who almost certainly weren't around after the hundreds of posts last time, Lee never DID grasp that two numbers multiplied together to give a product are FACTORS of that product. Still doesn't, as can be seen from his comment above. He still thinks the only way to get factors is through his special magical formula. That's cos Lee doesn't know what factors ARE. )

Still can't believe he wants to embarrass hisself thus.

That's an oxymoron as you well know. However, I was polite enough to deal with atheists first when you changed the subject to that. Now you've changed the subject to 'binomial expressions' and their factorisation, so I'm gonna set you straight there too. Just need you to co-operate and answer the outstanding question and two more even simpler ones. That can't be too much to ask, can it?

"Now you've changed the subject to 'binomial expressions' and their factorisation, so I'm gonna set you straight there too"

No, that was you went there first. At 4:24 PM, supra. (Which sorta helps answer the question I had lurkin’ in the back of my mind about whether or not you were just makin’ up stuff as you go, or whether you'd actually adjusted your own memory, convinced yourself of the stuff you were pretending. Not that it's really important for me to know whether or not you were deceiving yourself as well as the more casual readers. It was just a passing question in the back of my head.) More to the point: You were telling us that:

"Non-religion looks like superstition to the religious." Petes @ 2:03 PM, supra

You don't need me to answer questions before you explain that. You didn't like my explanation; let's see your

Nope. You mentioned the "mighty mystery maths" at 12:28 PM above, before I did. Well, those maths depended on an intermediate demonstration in order to lead yer simple self to the correct conclusion. That was by way of the demonstration of a mathematical fallacy, one step of which involved factorisation. You disappeared down obfuscatory rabbit holes at every opportunity, just like you are doing on this thread. Unfortunately for you, I can keep track of the thread of an argument very closely, regardless of yer wanderings. So, no, lets deal with one thing at a time. You painted yerself into such a corner with yer factorisations that you eventually just Jesuitically plain refused to perform a simple multiplication. Let's get over that hump before we accept yer bona fides in the current argument.

Unfortunately, my parents poisoned my mind with syfy and horror movies from the time when we were in the UK. I only broke free from their spell as a grown up.

lol! Right, right, blame the parents. I think syfy and horror movies are standard fare for kids. I was into that too. My friends and I even tried the seance thing. We did a good job of scaring ourselves silly. :)

I've always liked plays, but saw the one I mentioned only recently. Given some of your posts it was one I thought you might enjoy.

That's not to say I wouldn't still enjoy a good syfy or horror flick. One of the best horror books I read was "The Relic". The movie wasn't bad, but I liked the book better.

"You mentioned the ‘mighty mystery maths’ at 12:28 PM above, before I did."

Your ‘mighty mystery maths’ had to do with your oft repeated claim that you had some secret ‘maths’ that would explain why it was that Einstein didn't mean what he said when he said that the matter/conversion ratio was ‘independent’ of the rules of special relativity. First you were gonna uncork ‘em on us just any minute, and then you were gonna keep ‘em secret ‘cause I didn't act appropriately impressed with your threat to uncork ‘em on us. And then you switched back and forth between those poles and various positions in between several times, and never did unveil your mighty mystery maths. (Which of course were fictional from the get-go.)

But they didn't have squat to do with your failure to get your head around the factoring of a ‘difference of squares’ binomial square expression. Nothing at all to do with that. You went there all on your own.

And it's a mere fraud anyway. I flushed ya out out on the attempt to make agnosticism into superstition. You got nowhere else to go with that, so the only thing you can do now is throw up as much dust as you can and pretend you can't explain your position ‘cause it's too dusty. I knew you were gonna get here, eventually, and now you're here.

Now you'e gonna bluster some more and pretend you didn't just get burned to waterline again. And so it ends.

LOL. And that length piece of bluster explains why you won't perform a simple multiplication? And my "mystery" maths are apparently so unmysterious that you know they're unrelated to this multiplication? There's a simple way to find out, of course. But you won't go there. Why's that?

"I flushed ya out out on the attempt to make agnosticism into superstition."

Nope. Ya made one patently ridiculous claim about me confusing agnosticism with atheism. When that fell flat ya brought up the mystery maths. We haven't even touched the agnosticism claim. We'll get to it right after the simple multiplication.

"And that length piece of bluster explains why you won't perform a simple multiplication?"

Want the short version? The 'mighty mystery maths’ had nothing to do with the argument about binomial squares nor the appropriate factoring of same. The ‘mighty mystery maths’ dealt with an entirely different subject. The subjects did not intersect nor overlap. Petes opened the subject of binomial squares and the appropriate factoring of same, and now denies that he did. That denial was an open and intentional lie. Nothing short of that. Not a misremembering; not a misunderstanding. Just a simple lie outright lie for Petes to hide behind.

(Did ya follow it that time Lynnette? I could expand a little bit if that's too short a version.)

Lee's still havin' the same difficulty followin' the argument as he always did. The connection was very simple: 1) Lee alleged that Einstein's statement of the mass energy equivalence had nothing to do with certain earlier derivations in special relativity. 2) I set out to show the dependence of the mass-energy result on the constant speed of light, but Lee couldn't follow the maths. 3) I simplified it by showing how a different logical argument depends on the validity of all the previous steps in the argument. The example was verbatim quoted from Wikipedia (although Lee didn't know that to being with). 4) Lee claimed that not only I, but Wikipedia, was wrong. He "proved" it by claiming that c(v - c) were not factors of v - v^2. He's stuck to his guns ever since.

An intelligent five year old could multiply c(v - c). Lee won't do it, cos the final nail in his coffin is a demonstration that multiplication and factorisation are the same arguments in reverse. Instead, Lee got hung up on an Interweb article talking about factors of the different of two squares, and childishly took it to be all there was to say on the subject.

That's the whole story. That's why Lee won't do the simple multiplications. That's how it's connected to the Einstein thing. That's why Lee's a dunderhead and a liar and fraud to boot. All of this is straightforward to fact check. That's why Lee has to obfuscate.

It's still a lie. And Petes knows it's still a lie. And I know it's still a lie. And the posting timestamped 3:00 PM are simply embellishments on the lie.

Big surprise! It ends with Lee STILL refusing to do the simple multiplication. He probably remembers how embarrassing his factors were ... the ones that he wasted weeks insisting we're the only valid ones. He has one great talent, that's for sure. Ain't maths or philosophy though.

Now that you've doubled down on the lie, and we both still know it's a lie, and it being highly unlikely anybody else gives a damn, we can return, now without the distractions to what actually was the point before you went looking for diversions. To wit:

"You were telling us that:

"Non-religion looks like superstition to the religious." Petes @ 2:03 PM, supra"

"You don't need me to answer questions before you explain that. You didn't like my explanation; let's see yours."

Are you telling me you DIDN'T insist that vc - c^2 HAD to be factored as the difference of two squares, even though it's no such thing. Are you actually claiming that?

I rather doubt you're going to repent and confess. So, that conversation is pretty much over. You mistake me for someone who cares further.

You told us that:

"Non-religion looks like superstition to the religious." Petes @ 2:03 PM, supra"

That statement looks like foolishness on its face: I'm content to leave it lookin’ like that. If you've got nothing further to say on the subject then we're pretty much done here. I'm content to leave ya there.

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ Post Script: You've been noticeably agitated for a whole day now, excitable. Since ya got flushed. It shows. A lagniappe to leavin’ ya right there.

Christ (excuse the pun) Lee actually had the answer there and proceeded to mess it up. He's an embarrasment.

@ PeteS

A pure atheist cannot claim to base his system of belief on 'proof' since as Lee noted, he'd have to engage in the ultimate proving of a negative ... ie, proving that there is no God. Clearly that's impossible.

What is possible however, is examining what OTHERS have claimed as being proof for God and discarding those possibilities. Frankly the Bible itself was what turned me into an atheist agnostic.

Naturally, I too cannot prove God conclusively does not exist.

LOL. Everyone's favourite Jesuit has spent an awful lot of time saying how the discussion is over, and none at all addressing his embarrassing math faux pas.

Bruno, agreed (although I would say that makes you an agnostic, rather than an atheist agnostic). "Pure" atheism, as you call it, is illogical -- as illogical as scriptural literalism. Both involve wilful ignorance of the evidence. My guess is there are very few "pure" atheists. Unfortunately there are quite a lot of scriptural literalists, at least in Lee's part of the world, and I can see why people would be irate about attempts to have creationism etc. taught in schools. I would be too. On the other hand -- from where I'm coming from -- I see a lot of irrationalism on the so-called "non-religious"/agnostic side. Everything from homeopathy and quack science/medicine to syncretic mixtures of eastern "spirituality" and pop psychology. Richard Dawkins has bemoaned a rising tide of irrationalism, but in my experience most of it's coming from the agnostic, not religious, camp. Most of my religious pals (and certainly for me, for my own part) have a very scientific/rational outlook on things. I attribute it to an expectation of order in the world, based on its having been "designed".

"…an awful lot of time saying the discussion is over, and none at all addressing his embarrassing math faux pas." Petes @ 7:54 AM

I'll pass for now your foolishness regarding the imaginary ‘math faux pas’. The point of beginning was this:

"Non-religion looks like superstition to the religious." Petes @ 2:03 PM, supra

There is nothing there that would benefit from the application of some math. If you choose to leave that hangin’ out there naked and stupid, I have no great objection. (I wouldn't try to defend that if I were you either.)

PeteS, it all boils down to definitions in the end. When I say atheist agnostic I mean somebody who doesn't believe in a God, believes that on the balance of the evidence that there is no such thing ... but who also accepts the fact that it is impossible to prove the non-existence of God.

I disagree that atheists/agnostics are primarily responsible for quackery and so forth. That sort of thing in my experience is rooted more in New Age mysticism than atheist principles. Having said thus, however, the only homeopath I have encountered personally was a Christian and yes, against logic, his medicines seemed to work. Go figure.

Bruno, I agree, it comes down to the definitions. That's why I rarely use the term "atheist" myself. I prefer the term "dogmatic materialist" for someone who insists (in spite of the contrary evidence, in my view) that the material world is all there is. Apart from this piece of illogic, the dogmatic materialist is likely to reject both the mystical and the supernatural.

The agnostic is a whole other kettle of fish. Most agnostics I know are only agnostic with respect to "traditional" religion. They may be entirely embracing of the New Age (although that is such a broad church as to almost defy definition) yet still profess to be "agnostic".

Regarding your homeopath, I'd put that down to credulity on your part. Bet his stuff wasn't subjected to exhaustive double blind trials. The Christian aspect doesn't surprise me though. Many Catholic nuns (a dying breed) are reiki practitioners. I certainly wouldn't say the New Age is the exclusive domain of self-professed agnostics.

None of that addresses the assertion that a lack of religion ‘looks like’ superstition to the religious, i.e:

"Non-religion looks like superstition to the religious." Petes @ 2:03 PM, supra

Now that Petes has outclevered himself by denying his original destination for that assertion (See Petes @ 9:01 AM, supra.), he's left with a free-standing stupidity and no place to go with it.

LOL. Lee's still hopin' against hope he can make some statement of mine co-equal in stupidity with his monumental mathematical cock up, "jes' cos' he says so". Also seems to hopin' to muscle back in on the conversation now that Bruno has been civil enough to engage.

Wrong on all counts there Petes. You have a free standing stupidity hangin’ out there. That's the one that got you into this thread. Come the end of the thread here and you still ain't fixed it, and ya ain't gonna. Ya outclevered yourself and ya got nowhere to go with it now. I'm just enjoying that.

Post Script:

By the way, you'll notice that the 11:21 posting was not directed to you. It was about you, not to you. You should feel free to shut the hell up just any ol’ time now. (No, I'm not lookin’ to get back in on a conversation with you.)

Woohooo! Ole Lee's gettin' mighty ratty. Thanks for the offer, but it's quite ok -- I already feel free to do whatever the hell I like.

The comment that got me into this thread was never debated, due to yer obfuscations. Coulda been interesting, but not with you obviously. So yer claims about its cleverosity look pretty lame, wouldn't ya think?

"The comment that got me into this thread was never debated…"

Yeah, I know. I'm cool with that too. Leave it hangin’ out there as is, be fine with me. Ain't like that comment exactly makes ya look the genius ya know.

[petes] "Regarding your homeopath, I'd put that down to credulity on your part. Bet his stuff wasn't subjected to exhaustive double blind trials."

Nope and nope. I took his little white pills and water drops and a couple of days later I was much better. That said, there's no actual proof that it was that medicine that did the trick ... but it was a pretty unlikely coincidence. Objectively homeopathy shouldn't work at all, since I'm well aware of the methods that are used to make the final product.

"The great secret of doctors, known only to their wives, but still hidden from the public, is that most things get better by themselves…" Lewis Thomas―The Medusa and the Snail

Objectively, homeopathy should work at least as well as placebos, and that's a lot more than "not at all". That's why proper clinical trials are the only criterion by which we should judge if any given thing works.

"Of course not. (That OCD thing of yours must be a real bitch for you here, now that the audience is gone.)"

Oh no, the joy of OCD is that it doesn't need an audience. Anyway, until you give up tryin' to get the last word in, there's always an audience of one.

Oh yeah, sure. Perfectly sensible and verifiably accurate statement. I'm more than happy with how it looks.

How about you? Wanna provide different factors for vc - v^2? Wanna change yer opinion on how only the "difference of two squares" method can be used? Wanna tell everyone how you concluded that vc was a square?

Wanna remind us how the Wikipedia page on Mathematical Fallacies -- which has been reviewed over 1000 times over eight years -- is wrong, and the great mathematical genius Lee C is right jes' cos' he says so? LOL.

As you know and I know you're lying about the math and factoring stuff, just makin’ up the story now as you wished it had gone down then, and as it's hardly likely anybody else gives a damn anyway… It would seem that now's the time for you scratch that OCD itch of yours. I'm gonna let you get in the last word. (You might want to take a few minutes to consider it and make an attempt retrieve some particle of your credibility. But, I'm pretty sure you'll blow your last shot with more posturing instead.)

I'd remind you that there is also a Wiki page that's actually on the subject of factoring that did get it right. Neither of us have forgotten that. Although you choose to pretend.

See step 4, labelled "Factor both sides". You maintained, over the course of hundreds of posts, that the right hand side factorisation was wrong, and you even provided several (different) attempted solutions.

Ok, now show us the Wikipedia page on Factorisation that says that the above step 4 is wrong. Ain't that many Wikipedia pages on factorisation, so it's not like it's a big secret. But it'll be interesting to see you refuse to provide a reference here, just like you refused to do the damning multiplication earlier.

You keep claiming I'm lying about yer laughable attempts. You can refute it by just providing the link. Seems so much easier than just stonewalling each time until the audience leaves. I mean, that's kinda embarrassing, is it not?

Just in case you wanted to use your promised last shot to do something other than trying to make sure it's not your last shot, something besides tryin’ to troll me back out into a fight you lost long ago and want to re-fight now in hopes of a better outcome… I'll ignore the above posting just this once and give you another shot at a wrap-up… Or, we can just look at that as what you wanted to write nce you were assured that you'd not have to face a reply. Your choice. You want that 1:46 PM to count as the one I promised not to reply to, or you want to take another shot at a parting shot?

So, you still maintain that Step 4 RHS was not a valid factorisation of step 3, and that you can't (a.k.a won't) multiply out the RHS of step 3 to get that of step 4. That's still yer position, chump? Or is it that you've realised that you were posting idiotic drivel for 300 posts, and have painted yerself into such a corner you can't even allow it to be mentioned anymore? Could still be educational for ya, if we followed it through to its relevance to special relativity, but I can't see ya goin' there. Too much loss of face. Oh well.

Feel free to go there yourself. Explain the relevance. I'll watch along with any other readers you might still have. (Countin’ your 1:46 PM as your free last shot, on account of I have to count one of them, and you neglected to choose between them yourself, so I have to do it.)

LOL. You want me to provide the same explanation again, so that you -- who don't actually understand what factorisation is -- can just deny things written down in black and white? There's ignorance, and there's invincible ignorance, and then there's somethin' that afflicts you which is on a whole different level.

Firs you couldn't explain why agnosticism looks like ‘superstition’ to you unless I first answered a lot of questions you wanted to fuss over. (Later you decided that it was self-evident and needed no explanation.) Now you claim that your misunderstanding of the standard factoring rules for binomials and how it supposedly relates to the theory of special relativity (to which it does not in fact relate) can't be explained unless I answer a bunch of tangential questions about which Wiki page was right and which was wrong.

I'm beginning to see a pattern here. However, I'll just ignore the pattern for now. And go to the last point you tried to make.

"Could still be educational for ya, if we followed it through to its relevance to special relativity." Petes @ 2:28 PM, supra

You're fuckin’ bluffin’. You got squat ‘cept bluster and bluff. You cannot figure out how to make your math riddle relevant to special relativity. Go ahead. Call me on it! Set out to administer that ‘eduction’ you so clearly threatened. Follow through on that threat. I'll follow along. No problem there.

You just got your bluff called; put or fold. Your choice.

There's a lesson here for ya Bruno. You should quit tryin’ to bail this fool out of the messes he makes. Ths isn't the first time that you prematurely tried to prop him up as a winner only to have to watch as he came slowly unhinged.

"You're fuckin’ bluffin’. You got squat ‘cept bluster and bluff."

Well that's not a very polite start to your request.

"You cannot figure out how to make your math riddle relevant to special relativity."

Not only can I, I have actually done it several times, the latest on this very thread. You don't have the mental equipment to see it, but I'm still willin' to lead y'all through it in baby steps, so that y'all can follow it, on the assumption that yer capable of learning it.

"Go ahead. Call me on it! Set out to administer that ‘eduction’ you so clearly threatened. Follow through on that threat. I'll follow along. No problem there."

Ahh, but there is a problem. Y'all have demonstrated y'all's inability to follow the argument so far. That means we have to look at y'all's problems and hangups in detail. No point me continuin' on when you are already stuck at our very first point of departure. So y'all have to answer certain questions along the way, to check y'all's understandin'. Otherwise the endeavour is pointless.

If y'all is acceptin' of that approach I will happily continue. In other words, you forego yer obstinacy and paranoia and I will forego the jibes, and we will both take it in steps. Contrary to y'all's oft-voiced suspicions, I am ready, willin', and 110% able.

Obviously, the first step is gonna have to be the unpicking of y'all's misunderstanding of factorisation. No way round that. But it's y'all's chance to unpaint yerself outta that corner.

"I have actually done it several times, the latest on this very thread…"

In this very thead? Would that be before you first wrote that you could do that, but didn't (2:28 PM)? Or have you an imaginary posting been wanderin’ ‘round in your head some time since then? (I get the impression that you're hopin’ somehow that if you make an outrageous enough claim somewhere along the line then I'm going to get angry or emotional, or something, and that's what you're really shootin’ for, just to know you got under my skin is the best you're hopin’ for now. On the other hand, there's an outside chance you're just losin’ your grip on reality, but that'd not be my first guess.)

I called your bluff; put ‘em on the table or don't. Your choice. You don't get to negotiate for terms after your bluff has been called; that ain't how it's gonna play. Show or fold. Remains your choice.

Where is this bluff that you are supposedly callin' me on? I said, and I quote: "Could still be educational for ya, if we followed it through to its relevance to special relativity, but I can't see ya goin' there. Too much loss of face."

Followin' it through means goin' through it step by step so y'all are able to follow it. If y'all think I am bluffin' then call the actual bluff, not one of y'all's imaginin'. Had too much of you backtrackin' on the original thread, when you agreed with somethin' but then suddenly didn't when y'all realised yer own self-contradiction. Ain't interested in that approach. If y'all think that's a bluff, there's an exceedingly simple way to find out.

I know I promised to not interrupt you unnecessarily. But, it may be necessary here. Tthat seems a most curious place to stop. Have reached the end of your step one?

Well, then… You're nowhere close to demonstrating the relevance of your little math trick to the Theory of Special Relativity. You have a long way to go. I suspect you've stopped there in hopes of taking off onto a tangential argument, and I'm not interested in having a tangential argument. But, I follow you so far. It's been easy so far, ‘cause you haven't actually gone anywhere as of yet. But, there's still time:

"Feel free to go there yourself. Explain the relevance. I'll watch along with any other readers you might still have." Lee C. @ 2:39 PM, supra

"Set out to administer that ‘educ[a]tion’ you so clearly threatened. Follow through on that threat. I'll follow along." Lee C. @ 4:18 PM, supra

So, I'm following along so far. You may proceed ahead on whenever you're ready. (Or, I suppose, you may squat there instead, if that's what you choose to do.)

"Well, then… You're nowhere close to demonstrating the relevance of your little math trick to the Theory of Special Relativity. You have a long way to go."

That, of course, is pure supposition on your part. You don't know whether I am close or not. Remember the "mighty mystery maths"? If they are a mystery, as you claim, then by definition you don't know if I'm close to a demonstration yet or not.

That said, a demonstration can only be such if it is clear to the audience (i.e. you). We've already established that yer lack of mathematical understanding prevents you from reasoning this out for yerself -- otherwise no demonstration from me would be necessary. It's partly clear to me, being as my maths is superior to yours, where your misunderstandings lie. But to be sure we cover all your educational needs, it will be necessary for you to show your evolving understanding at various points along the way.

That's why step one ended with a question for you to answer. If I provided the answer, then there seems little doubt that you would say the same as you said last time, to wit: "that's just wrong". If you wish to progress, your answer is required so that we can explore how your answer is incomplete and/or wrong, on the way to painting the bigger picture.

My math skills are so-so. Way above average but nowhere near those that "get it". I did struggle through the first year of civil engeneering with the math courses: linear algebra, analysis in one variable and analysis in several variables (never managed to complete the last one with a passing grade), then I flunked out and got into basic computer sience which was way easier. I get the feeling Pete has maths knowledge on par with a civil engineer graduate, and knowing how hard that is I'm not gonna get into a pissing contest with him in these matters. But the stuff you've discussed in this thread seems like pretty straight forward algebra, so far.

Not quite, Marcus, although your choice is understandable. The factors are (√(ab) + b) and (√(ab) - b). Factored down it reads (√(ab) + b) × (√(ab) - b)

No Marcus, factors are numbers which when multiplied together yield a product. The product of a and b, i.e. a × b, is ab, not (ab - b²). Any numbers which multiplied together give the desired product are factors. That's the definition* of a factor.

* It's usually stipulated also that (a,b ϵ ℤ), but we will come to that additional qualification in due course.

Are these the only factors of ab - b²? Well clearly they are not, since I can easily generate any number of factors I like from the one above, e.g.:

(2(√(ab)) + 2b) × (½(√(ab)) - ½b)

Let us constrain the answers a bit. Suppose a and b are whole numbers, whether positive, negative or zero. In other words, they are integers, which we denote by (a,b ϵ ℤ). What are the whole number (i.e. integer) factors of ab - b², if any? Are the following still factors?:

The E is an epsilon, denoting "element of". The Z is normally written as "blackboard Z" or "double-struck capital Z", denoting "the set of all integers".

[PeteS] ... assuming he doesn't delete the entire conversation ;-)

lol!

Well, he let us go on and on before so he might not really care. And it's a pretty innocuous argument in an old comments section. Besides it looks a little empty without comments.

I haven't checked to see if he's managed to copy back any of the old comments sections that went missing with the changes.

Ok, looks like we have a fundamental gap in your understanding to be bridged.

Do the variables a and b represent anything in particular? Suppose I said that a represented an avocado, and b represented a banana. Would the following statement make any sense?:

The factors of ab - b² are (√(ab) + b) × (√(ab) - b).

I'm not sure what the product of an avocado and a banana would be, let alone their square root. Instead, a and b must be certain classes of things for which those mathematical operations are defined. Since you have already given us the factorisation, what classes of things did you have in mind for a and b? (They can't be just any old thing, since we can see it doesn't work for avocados and bananas). They must represent some class of thing for which the operations you used are defined. So what is that?

"variable- is a letter that represents an unknown number"

I believe we may safely exclude avacados and bananas from consideration. This sort of silliness is why I generally decline to answer intermediate questions for you. (One may assume Marcus was generally seeking enlightment and not playing games--which is why I stopped to answer his question. Obviously, the same assmption cannot be made concerning you.)

Do you suppose you can proceed without further farce?

"variable- is a letter that represents an unknown number"

I believe we may safely exclude avacados and bananas from consideration. This sort of silliness is why I generally decline to stop and answer questions for you.

Do you suppose you can proceed without further farçe?

"Do you suppose you can proceed without further farce?"

With your co-operation, yes. Let's look at your statements:

a and b are variables. These are integers: […-3, -2, -2, 0, 1, 2, 3…] ... [A variable is a] symbol for a number we don't know yet.

Hopefully you will notice that the things you listed as integers are numbers. A variable is -- as you pointed out -- a symbol for a number. It is possible that the number is an integer. Then we would refer to is as an integer variable. Maybe you didn't realise all of this until you Googled those definitions. Or maybe your comment at 1:35 PM was itself a farcical attempt to suggest that something could not be both a variable and an integer*. Either way, equipped with your new understanding, revisit my statements and questions of 1:14 PM.

(* That is, to be precise, a variable representing an integer; it is more usual to simply say that the variable is an integer).

And how does the incorrectness of my statement follow from your definition of a prime number? (I am not sandbagging either -- I believe your statement is evidence of another gap in your understanding).

Explaining it gets me into jargon I can barely remember and may use incorrectly and then I'll have to listen to your bullshit about how knowing the jargon means ya got the concept covered, and I've had enough of that long time ago. Let's go at it another way then: (I hope I don't discover that I should have gotten a pencil and paper for this.)

Numbers greater than the number being factored are not factors of that number.

You will notice that none of the examples have factors of absolue value greater than the number being factored. I.e: 24 is not a factor of 12 even though 24 × ½ = 12

You will find that it does, indeed, work out to the right answer of -42.

While you mull over that, I will accept your restriction that the factors must not be greater than the number being factored. Give me a moment and I will generate you an infinite number of factors that obey that restriction. Meanwhile you can redo your sums and, if you like, get back to me about why your definition of a prime proves me wrong.

Just a note of caution -- when you pluck definitions from the web, there will often be assumptions about the classes of numbers involved. We will come back to this, but to take one of your examples from earlier:

"Prime Number - A whole number greater than 1 which has exactly two factors, 1 and itself."

Well, that's not right is it? I know 3 is a prime, but it has factors 1 x 3 and -1 x -3. So the definition was incomplete because it failed to say that it has exactly two factors which are Natural numbers.

This lack of attention to classes of numbers is at the root of one of your problems.

"(2√7 + 14) × (½√7 - 3.5) You will find that it does, indeed, work out to the right answer of -42."

Damn; one of these days I'm gonna learn to not be doin’ that stuff in my head.

However; seems we do agree that there are different rules for different types of factoring, or at least that there are different types of factoring. I think that's sufficient for now.

However, all of this is wandering quite far off topic. If you like, I will explain your very original misunderstanding about factorisation. Alternatively we can work through these various sub-topics if it ultimately helps your understanding. If you like I will explain why it is trivial to generate an infinite number of non-integer factors of any number, rather than give you the complicated looking equation in the previous comment.

Ok, before we move on, let's just address your comment of 2:45 PM. Do you still maintain that the definition of a prime number somehow invalidates my statement? If so, how?

Also, can you answer my questions about integer factorisation at 2:32 PM?

"Damn; one of these days I'm gonna learn to not be doin’ that stuff in my head."

If you were able to look at this the right way, you wouldn'a had to work it out in your head or on paper. You wouldn'a had to work it out at all! You would've been able to see that it was true by definition. Might get ya to that point yet.

I see you've added a n < (ab - b²)/(√(ab) + b) to your theory. Just noticed that in passing.

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ "[C]an you answer my questions about integer factorisation at 2:32 PM?"

I think so. The questions were:

"what are the integer factors of ab - b²"

Answer: none

"Are the following still factors?: (√(ab) + b) × (√(ab) - b)

Of (ab - b²)? Yes.

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ "You would've been able to see that it was true by definition."

If you were that good you wouldn't be applying the wrong definitions.

"Proper factorisation -- factoring a number into its positive factors Prime factorisation -- factoring an integer into its (unique) prime factors Integer factorisation -- factoring an integer into its integer factors Rational and real factorisation -- similar to integer factorisation for rational and real numbers respectively."

I see factoring definitions for ‘a number’ (twice--first and last), and ‘an interger’ (the two in the middle)). (ab - b²) is neither an integer nor a number; it is a polynomial expression, specifically a binomial expression

I see you've added a n < (ab - b²)/(√(ab) + b) to your theory. Just noticed that in passing.

Yes, that's perfectly allowable. All I was offering was an infinite number of factors, based on your factors of (ab - b²). My factors are based on multiplying your factors by n and 1/n respectively. I also happen to be saying that "n < (ab - b²)/(√(ab) + b)". Does that cause you a problem? There are still an infinite number of values of n, and therefore still an infinite number of factors.

I can simplify this for you, if you like:

Suppose we have two numbers m and n. Then m and n are factors of the product mn (obviously):

mn = m x n

Equally obviously:

mn = m x n x 1 = m x n x q/q

... where q is any other number.

Therefore:

qm x n/q = mn (by the associativity of multiplication, which I will explain if you don't get it)

... and there are an infinite number of possible values for q. If you want to ensure that none of the factors is bigger than the product mn, then just constrain q to be less than n. There is still an infinite number of values*.

That's all I did with your factors of (ab - b²). Your factors were themselves sums, so it looks a little more complex, but it's the same thing.

* Note that q is not necessarily an integer and therefore neither are the factors. If m,n and q are constrained to be integers, there is not an infinite number of values of q. There may be zero, but not necessarily so, a point which will be important later on.

"I think so. The questions were: "what are the integer factors of ab - b²". Answer: none"

Ok. Here we have to check your understanding of the meaning of algebra. You do realise that when you say that there are no integer factors of (ab - b²), that you are saying, for ANY POSSIBLE values of a and b, the quantity represented by (ab - b²) has no integer factors? It doesn't just mean that you haven't managed to find a formula on the internet that easily gives them to you.

For instance, let a = 10 and b = 8. Then (ab - b²) = 16, which definitely DOES have integer factors. Do you perceive an incongruity between this fact and your statement about the lack of integer factors. (I am not being a smartass here).

I'd love to simply things. This is as good a time as any. Who besides you thinks that there are ‘an infinite number of factors" for a binomial expression?

"I see factoring definitions for ‘a number’ (twice--first and last), and ‘an interger’ (the two in the middle))."

Correct. The definitions overlap. For example, prime factorisation IS integer factorisation, but not vice versa. The integer factors of 12 are 1,2,3,4,6 and 12. The prime factors of 12 are 2 and 3, which happen to be also integer factors. There is no anomaly here.

"(ab - b²) is neither an integer nor a number; it is a polynomial expression, specifically a binomial expression"

This, I am afraid, is something you will have to get over (unless you are being intentionally obtuse). If b represents an integer, it is perfectly common parlance to say that b is an integer. If a and b both represent integers, then (ab - b²) also represents an integer. In common (and I mean common in formal mathematics) parlance, (ab - b²) is an integer.

"In common (and I mean common in formal mathematics) parlance, (ab - b²) is an integer."

And again, who besides your own deluded self believes that? I wanna see a link. (I may be a little rusty on my arithmetic, but I ain't dumb enough to buy this one.)

"Who besides you thinks that there are ‘an infinite number of factors" for a binomial expression?"

I'd imagine that question implies that you have given up trying to follow the maths. You're about to resort to an appeal to authority, by citing internet references. I'm trying to explain to you why your internet references include some hidden assumptions that you didn't know about. If you follow the argument, you will come to understand them. If you resort to just citing references that you don't know enough to properly understand, well then you're gonna just look stupid (to everyone but yourself, perhaps).

However, even if you can't follow the argument, you can at least perform your own sanity check. If you at least understand the valid use of algebra, you can take the example of the binomial that we have been using, feed in values for a and b, and observe that there are indeed an infinite number of (not necessarily integer) factors. You can also observe that for some values of a and b, there are also integer factors, a fact you denied. That, at least, should give you pause for thought.

"In common (and I mean common in formal mathematics) parlance, (ab - b²) is an integer."

And again, who besides your own deluded self believes that? I wanna see a link."

Let's first use my entire quote in context:

"If a and b both represent integers, then (ab - b²) also represents an integer. In common (and I mean common in formal mathematics) parlance, (ab - b²) is an integer."

I truly hope you are not asking for proof of that. The product of two integers is an integer. The square of an integer is an integer. The difference of two integers is an integer. Surely, you accept those facts and can combine them to see the truth of the above statement? If not, I fear for your ability to understand any of this.

"I'd imagine that question implies that you have given up trying to follow the maths."

Think again then. I was challenging your mis-definitions and your applicati0on of the wrong rules based on those misdefinitions.

"There is no anomaly here."

It's not a question of an anomaly. It's about you trying to apply the wrong rules--you're trying to factor a polynomial expression as if it were a known number, real, rational, or integral. It's not a number it's a polynomial expression..

"If a and b both represent integers, then (ab - b²) also represents an integer."

Rather (ab - b²) represents a formula, a calculation that can be solved to get an integer. (ab - b²) does not represent an integer--it is a formulaic represention of a calculation, as yet unsolved. After it's solved, then you have the integer.

I.E: ((8×10) - 10²) is formula, it is not an integer. These are integers […-2, -1, 0, 1, 2,…]

"I.E: ((8×10) - 10²) is formula, it is not an intege"

Or, maybe it's a calculation, seeing as it has no variables. I'd have to look that one up. In any case, it is not an integer. These are integers […-3, -2, -1, 0, 1, 2, 3,…]. I don't have to look that one up.

And Petes has quit his furious posting. One can only suspect that he's off googling furiously in place of the posting furiously. I'm gonna get back to the real world for awhile then. Got things to do. But, never fear Marcus, I shall return. May be morning before I get back though.

"you're trying to factor a polynomial expression as if it were a known number, real, rational, or integral. It's not a number it's a polynomial expression"

Here, and in the subsequent three comments, lie the root of all your lack of understanding.

Algebra is about the symbolic manipulation of numbers. Anything that we say about a variable, we are also saying about the number that it represents. If it is an unknown, then anything we say about the unknown, we are saying about all the possible values it could represent. That is the whole value of algebra -- that we can make generalised statements about unknowns. That is why we can interchangeably say an expression represents a number and an expression is a number. Anything we say about the expression is true of the number it represents. If b represents the number 8 then b is an integer because 8 is an integer and the polynomial (b + 3) is also an integer because 8 + 3 is an expression representing an integer. Let's suppose we don't know what b represents, except that it is an integer. Then b^2 is an integer, because all integers squared yield integers. Lets suppose that we only know that b is a number. We still know that b^2 is a number, because all numbers squared are numbers. If b is a banana, then we are out of luck because algebra doesn't deal with bananas.

Let's look at your own example. You were able to come up with two polynomials which were factors of another polynomial, without knowing or caring about the values of the variables involved.

But how do we know the statement you made was true? You followed some rule you found on the internet. How do we know that's true? Let's ignore that just for now, and instead ask a much simpler question: "how might we know that your statement is false?"

Well, I think you would accept that I could disprove your statement as follows:

1) Choose any values of a and b 2) Calculate the correponding values of the factor polynomials 3) Calculate the corresponding value of the product polynomial 4) Multiply the calculated values of the factor polynomials and compare to the calculated value of the product polynomial 5) If they are not equal, your statement is false.

You used this exact numerical approach yourself to try to falsify my factorisation.

In essence, your claim about your factors is that they are algebraic expressions representing numbers, and those numbers are factors of the number represented by the original polynomial.

Thus, if you claim there are no integer factors of the polynomial (ab - b²), you are making a statement that the polynomial cannot represent a number with integer factors. In fact, you only have to take any integer values at all of a and b and your statement is immediately shown to be false.

Indeed, your own factorisation method using the difference of two squares (which you have always erroneously assumed to be the only possible factorisation) shows your statement to be false for any values of a and b where ab is a perfect square. Take the values 2 and 8, for instance. Your factors are both integers.

And no, (having read your comment) Petes hasn't quit his furious posting. Petes is so bamboozled by how fundamental your misunderstanding is, that, in the hope of conveying the truth to you in simple terms that you might grasp, he wrote and rewrote the above several times. Not one Google result was harmed in the making of it. I'm still not expecting you're gonna get it. I think your misunderstanding is too fundamental. You're still gonna just say "but, but, but, it's a polynomial not an integer".

Perhaps we can try one last thing. Suppose I take the question from 2:32 PM, to wit:

Assuming that a and b are integers, what are the integer factors of ab - b², if any?

.. and I rephrase it thus:

Assuming that a and b are variables representing integers, what are the factors of ab - b² which represent integers, if any?

Now you do not have to get hung up on whether something is a polynomial or a number. In fact, I am asking if you can show algebraically that the number represented by the polynomial (ab - b²) has factors which represent integers? By algebraically, I mean that you still deal with the variables a and b, and not with any particular values of them. You must show that there ARE integer factors, without citing any particular example. Clearly, your difference of two squares method does not guarantee integer factors because the square root of ab is not guaranteed to be an integer for all values of a and b even given that a and b are integers.

This also highlights an interesting point. We know that there are guaranteed to be integer factors of the number represented by (ab - b²) if a and b are integers (for reasons I explained earlier and can go through again if you wish). We also know that your difference of two squares method doesn't find them. That means that your approach does not find ALL the factors of (ab - b²). That on its own puts paid to your long time insistence that the difference of two squares method is the ONLY factorisation of the polynomial.

Here's another one to mull over. Consider the following proof that there is an infinite number of even numbers.

1) There is an infinite number of positive whole numbers. (We're taking this as axiomatic, although we could show it using the arithmetic sequence Tn = Tn-1 + 1, but we're trying to keep things simple)

2) For any positive whole number, n, there is a corresponding number, 2n, which is evenly divisible by 2 (i.e. even).

3) Therefore there is an infinite number of even numbers.

But hang on! How can we claim that 2n is divisible by 2 (i.e even)? Only numbers are even, and using Lee logic, 2n is a polynomial, not a number! Is there some other way of proving the infinitude of even numbers that is not equivalent to this one?

I just wandered back in to turn off the computer and found a long and winding road, middle of which was this:

"You followed some rule you found on the internet How do we know that's true? Let's ignore that just for now,"

Okay, first of all, I didn't find it on the internet. I just looked at your calculations and saw it was wrong and saw where. I didn't have to go to the internet until I started trying to find the terminology, the jargon, to explain it. As for how ya'll will know I was right… What more do you want than the fact that it always comes out right. (I got more, but I can't see that I need more.) It does not lead one into errors.

But the real kicker in your post was this part:

"Let's ignore that just for now,"

No. let's not. Tell ya what ya do. You find us the rules for factoring the variable a, or b or any other variable. Put up a link. You won't find one. You know why? It's cause ya don't factor variables. You can factor numbers; you can factor equations, you can factor polynomial expressions. You don't factor variables!. That's the difference (one of them anyway) between working with variables and working with numbers. So all your spin leading up to that wild ass claim that:

"…we can interchangeably say an expression represents a number and an expression is a number"

That just happens to be bullshit of the first order. We don't say that interchangeably, we can't, ‘cause it's not true. A math expression is not a number; it sure as hell ain't an integer. It may lay out how to reach a number, but it's not a number; it's at best the formula for finding a number, and that's as close as it gets.

And I'll be down for the evening now. Have fun lookin’ for that factoring a variable thing, trying to prove me wrong.

Clearly, you've gotten bored of following the argument, and just mean to pick out random sentences to argue with. You also didn't pay too much attention to making sure you picked sentences I actually wrote. Where did I suggest you can factor a variable? If you give me the variable b, and tell me only that it represents a number, there is no rule for factoring it. That's not to say the number represented by b has no factors, only that we have no way to find them in the absence of more information. If you tell me b represents an integer, I can tell you that it has integer factors 1 and b. I can't tell you what other integer factors it might have, nor is there a rule for finding them. If you give me the expression 9x, as in your example above, and you tell me that x is an integer, than I sure as hell can tell you that 1, 3, 9, and the integer represented by x are integer factors of the number represented by the expression 9x. I can find you rules for that, but do you really want me to teach you your "three times tables"? If you tell me x represents a prime then I can tell you that the numbers I just mentioned are the ONLY integer factors of the number represented by 9x.

By the way, it's gonna get pretty tiresome if I have to keep saying "the number represented by" just to satisfy your fantasy that a variable or polynomial expression isn't a number. Also, if y'all wanna get all hardcore about definitions, there are several I have been fairly loose on in your favour so far.

Firstly, any simple variable is a polynomial. For instance, x is a polynomial of order 1, with coefficients 1 and zero. So your statement that: "You can factor numbers; you can factor equations, you can factor polynomial expressions; you don't factor variables!" is bullshit off the bat, as you would say.

Second, we have been loose with the definition of polynomial factorisation. That is defined as the process of decomposing a polynomial into irreducible polynomials. Your factorisation using the difference of two squares doesn't even produce polynomials! That's cos by the strict definition, a polynomial may only contain integer exponents. Your square roots in your factors are non-integer exponents. I was gonna explain all this to ya in gentle steps, but seein' as ya want to get all pissy, ya can go and Google the definitions to confirm I am right. Your famous difference of two squares isn't actually a valid polynomial factorisation at all in the case at hand! I was lettin' y'all away with it because it's not germane to the demonstration of how to do things right. If y'all would prefer that I just prove you wrong, there you have it.

If ya wanna get back on track, then you better start comin' to some sort of idea of what it means to factorise anything. You are doin' the same process whether you are factorisin' numbers or polynomials. (Note for the picky: I did NOT say you do it in the same way, just that it is the same process). Furthermore, when factorisation is discussed, it MOST COMMONLY refers to integer factorisation. If you wanna be picky, then start mentioning which type of factorisation you are discussing. Your difference of two squares is a handy one for finding integer factors of a particular form of binomial when the variables involved ARE KNOWN TO BE INTEGERS. It's fuck all use for anything else. Your bastardised version of it doesn't produce integer factors, EVEN WHEN the variables are known to be integers, and, as I've pointed out, it doesn't even produce valid polynomials and is therefore not a factorisation at all.

And just to tie up the rest of yer pissy post, in case y'all hypocritically moan that I am being over-picky about the definitions. Let's relax them and accept your factorisation for a moment. You said: "As for how ya'll will know I was right… What more do you want than the fact that it always comes out right."

Two points may be made about this. First, what the fuck do you mean "it always comes out right". You mean, when I choose values for a and b, and work out the corresponding values represented by your factors, and multiply them out, they come out to the number represented by your polynomial for those values of a and b. The only reason I ever give a rats arse about an algebraic expression is because any operations I perform on it will give exactly the same results as the same operations performed on the numbers. Your distinction between the algebraic expression and the number it represents is facile and pointless. I could equally argue that the written digit two is just a symbol (which it is) and not the actual number it represents. It's ALL symbols.

Second, you may well be God Almighty, as you seem to think, but I'm prepared to bet you haven't tried your factors for the infinity of possible values for a and b. We only need a single counterexample to show you're wrong (no matter how enraged that suggestion seemed to make you). But that's no problem -- I know perfectly well how to multiply out your factors symbolically, to show that you get the right result, without having to do it for all possible values.

I also gave you an infinite number of other factors, all of which work out perfectly when you multiply them out. Apart from the fact that they weren't generated by yer beloved "difference of two squares", what's yer problem with them?

Postscript: when I say "what's yer problem with them", obviously what I mean is for you to apply your own definition of correctness, which I quote: "As for how ya'll will know I was right… What more do you want than the fact that it always comes out right."

"Clearly, you've gotten bored of following the argument,"

What I'm getting bored with is you makin’ up stuff as you go along, just ‘cause you want it to be that way. Like this for instance:

"Firstly, any simple variable is a polynomial. For instance, x is a polynomial of order 1, with coefficients 1 and zero."

That's not true. x is not a polynomial. 9x is not a polynomial. (x - 1) is a polynomial. (9x - 7) is a polynomial. (The parens, or lack thereof are not determinative.) Both are binomials. (9x - 7 + 7y) is a polynomial (a trinomial). But x or 1x or 1x/1 are not polynomials. Google definition polynomial and first rattle out of the box, First entry tells us that a polynomial is:

"An expression made with constants, variables and exponents, which are combined using addition, subtraction and multiplication…***"

And it further tells us that 5xy² - 3x +5y³ - 3 is a polynomial, but that 3x is merely a term within the polynomial. (By the same token, neither x nor 1x nor 9x are polynomials.) First rattle out of the box and you're wrong. And you can't get your head around the concept that you're wrong. And you think you don't need any further authority than the pontifications of The Great and Wonderful Petes makin’ up stuff as he goes along is all you need. Yeah, I may be getting bored with that one.

So, tell ya what ya do. We'll go back to your founding error from way back when. You originally told me that you could come up with ‘hundreds of ‘factorizations’ (Brit terminology) for a binomial square expression. (I called bullshit on ya on that at the time.) The are a maximum of four (4) ways to factor one of those, not hundreds. So, you find some authority other than The Great and Wonderful Petes for the proposition that one can factor a binomial square expression hundreds of different ways as if it were a number or an integer (which it is not). You find me some authority for the idea that you can factor a binomial square expression n number of different way ‘where n < (ab - b²)/(√(ab) + b). You do that and I'll sit up and take notice.

Just for what it's worth, you're confusing two concepts. You seem to think that the Lorenz transformations are a factorization of some sort. They are not. In spite of the fact that it's sometimes referred to as ‘the Lorenz factor’, it's a progression, not a factorization. (I think progression is the right term, maybe I should look that up. Whatever, it's not a factorization at all.) Another example of you thinking that memorizing terms means you've got your head around the concepts. And it just ain't so.

Oh, and just by the way… Kinda a post script kinda thing… Second rattle out of the box and you're wrong a second time.

"Second… *** Your square roots in your factors are non-integer exponents"

This is not true either. √(ab) is not an exponent at all, much less is it a ‘non-integer exponent’. One would have to re-write it to get an exponent in there (of ½); i.e. √(ab) = (ab)^½., but that doesn't make the radical sign (√) into an exponent. And, even if that were not true, a ‘be that as it may’ type of thing; nobody ever said that (√(ab) - b)(√(ab) + b) was a polynomial. (ab - b²) is a polynomial. But nobody ever said it's root factors were polynomials. (I happen to think, off the top of my head, that's not true. For instance (6x - 3)(5x + 3) is not, strictly speaking, a polynomial I don't think. ‘Bout that time I just gave up tryin’ to parse your crap for all the crap it contained)

"First rattle out of the box and you're wrong. And you can't get your head around the concept that you're wrong. And you think you don't need any further authority than the pontifications of The Great and Wonderful Petes makin’ up stuff as he goes along is all you need. Yeah, I may be getting bored with that one."

There's somethin' y'all should understand here. Y'all are not gonna "win" this argument (whatever that means) through a Googlin' competition. All you are gonna do is end up lookin' incredibly fuckin' stupid, which is what y'all are lookin' right now. I told you that definitions tend to make assumptions and simplifications. The one about polynomials having additions and multiplications applies to the polynomial x, if you think of it as 1x + 0. Likewise, I told you (without doin' any Googlin', btw), it is a polynomial of order or degree one (because the exponent of x is 1) with coefficients 1 and 0, because there is one x and zero ones. That is not pontificatin', that is called knowin' shit. Your Googlin' disagrees? Then your Googlin' is wrong. Although it turns out that the only thing wrong is that y'all didn't read far enough. So follow that "more" link at the bottom of yer "first rattle outta the box" and y'all will find that it gives 3x as an example of a polynomial. See any additions in there, chump? A few lines later it gives 1 as an example. Any multiplications? Then follow yer "third rattle". It says "A polynomial is a monomial or the sum or difference of monomials". And it gives 9, x, and 9x as examples. Still feelin' bored now? ...or pretty fuckin' stupid?

"So, you find some authority other than The Great and Wonderful Petes for the proposition that one can factor a binomial square expression hundreds of different ways as if it were a number or an integer (which it is not)."

First thing I should point out is that the expression we are talkin' about is NOT a binomial square expression. I'm gonna let that one slide, as I have to date, on account of it is not (yet) germane to the argument, and lord knows I certainly don't need any extra examples of you lookin' pretty fuckin' stupid.

Second, I cite as my authority, the great and wonderful Lee C. Here is your definition of correctness: "As for how ya'll will know I was right… What more do you want than the fact that it always comes out right." You wanna change your own definition, go right ahead, be sure to let me know what the new definition is. Until then, I have given you a factorization. You worked it out and found it gave the right answer. Or leastways you tried to work it out and I corrected your mistakes, to show it gave the right answer. Do you now disagree it gave the right answer? (Warning: you're gonna look pretty fuckin' stupid if you do).

Then I showed you how to modify that factorization to give any number of other different ones. It did not give "n number of different way[s] ‘where n < (ab - b²)/(v(ab) + b)". That's just your misunderstanding. It used a number n, where n can have any value up to that limit, including fractional values of which there is an infinite number. Knowing that you were unlikely to understand this, I gave you a simpler example to follow. Looks like you did not bother your arse tryin'. As to me findin' a link for this -- don't be fuckin' ridiculous. I provided you a general proof. Do you think every specific example is gonna be on a Wikipedia page somewhere? Do you understand the concept of a general proof? It's kinda like when you learn that 1+1=2, and 11+1=12, you don't need a Wikipedia page for 21+1 'cos you have a rule for it. I gave you the general proof. If you'd like me to explain it again I will, seein' as you didn't get it first time round. But don't bother makin' ridiculous fuckin' demands for Googles at dawn in some internet duel.

"Just for what it's worth, you're confusing two concepts. You seem to think that the Lorenz transformations are a factorization of some sort. They are not.... etc., blah blah blah"

Oh fuckin' spare me.

There's one big mistake I am sensin' I've made. That is the mistake of thinkin' that because you are prepared to argue this thing, that you have even the remotest shred of knowledge of what y'all are talkin' about. Startin' to look like y'all have an itchy Google finger an nothin' else. So we're gonna have some new rules. When you don't understand somethin', y'all can ask politely for an explanation. Throwin' out random Google hits is a waste of everyone's time, and I've had enough of that shit.

(√(ab) - b)(√(ab) + b) is not a polynomial. (5 - 3)(5 + 3) is not a polynomial. (2 × 8) is not a polynomial.

I'm not particularly impressed with the argument that I should just quit lookin’ stuff up and just believe the too convenient fictions whupped up by The Great and Wonderful Petes instead.

And seen as we had overlappin' posts, I am gonna deign to reply one more time to yer inane shit.

"√(ab) is not an exponent at all, much less is it a ‘non-integer exponent’. One would have to re-write it to get an exponent in there (of ½); i.e. √(ab) = (ab)^½., but that doesn't make the radical sign (√) into an exponent."

Your square root sign, and an exponent of one half, are the same thing. Period. For an equally stupid fuckin' example 1+(-2) does not turn the addition into a subtraction. But they are the same thing.

"And, even if that were not true, a ‘be that as it may’ type of thing; nobody ever said that (√(ab) - b)(√(ab) + b) was a polynomial. (ab - b²) is a polynomial. But nobody ever said it's root factors were polynomials."

You obviously didn't follow the definition of polynomial factorisation. I suggested you Google it, but seem that you only Google your own shit. Your factors need to be irreducible polynomials. If we allow your square root shit, then there is no such as an irreducible polynomial because we can repeat your square root shit ad infinitum.

"(I happen to think, off the top of my head, that's not true. For instance (6x - 3)(5x + 3) is not, strictly speaking, a polynomial I don't think. ‘Bout that time I just gave up tryin’ to parse your crap for all the crap it contained)"

Those factors are a pair of polynomials.

You are in this way over your fuckin' head. I advise going back to basics. One way or another, I will not be entertainin' anymore of this obfuscatory shite.

Although, for "bored" I am readin' it that you realised your entire "first rattle out of the box" spiel was founded on you not botherin' yer hole to read more than one sentence. That's the only explanation for how yer own Googlin' doesn't even agree with ya. I take it y'all were never serious about tryin' to understand this shit (even had you been capable). I will remember that for future reference.

"So follow that ‘more’ link at the bottom of yer ‘first rattle outta the box’ and y'all will find that it gives 3x as an example of a polynomial. See any additions in there, chump? A few lines later it gives 1 as an example." emphasis added

I see that. And they've rather overstated the case there. (What was it you said about folks being too loose with their definitions sometimes?) It can be re-written to be a polynomial but it is not a polynomial standing by itself. They'er being too loose with application of the test for a polynomial i.e. that ‘A polynomial is made up of terms that are only added, subtracted or multiplied.’ and they're going on to work it up even further, to cover things that could be the products of addition, subtraction, or multiplication.

Eventually they come back to reality and do notice that:

"Polynomial comes form poly- (meaning ‘many’) and -nomial (in this case meaning ‘term’) ... so it says ‘many terms’"

Look at 1. How many terms do you see there? Look at x. How many terms do you see there?

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ "Your square root sign, and an exponent of one half, are the same thing. Period."

Nah; fer instance:.

5 × ½ = 2½ 5 × .5 = 2.5 2.5 = 2½

½ is a fraction; .5 is a decimal. A fraction is not a decimal, although they can yield the same results after all the calculations are made. By the same token a radical sign (√) is not an exponent, no matter how much you wish it were.

So, getting back to the ‘polynomial’ thing… I did a little more googling in spite of your warning that I must believe only what's told here by The Great and Wonderful Petes’, without any further authority And, you'll be happy that I did.

"Definition of a polynomial "Before giving you the definition of a polynomial, it is important to provide the definition of a monomial "Definition of a monomial: "A monomial is a variable, a real number, or a multiplication of one or more variables and a real number with whole-number exponents "Examples of monomials and non-monomials Monomials ― 9, x, 9x, 6xy, 0.60x^4y Not monomials y - 6, x-1 or 1/x, √(x) or x1/2 6 + x, a/x

Goes on to say that:

"Polynomial definition: " A polynomial is a monomial or the sum or difference of monomials. Each monomial is called a term of the poynomial "Important!:Terms are seperated by addition signs and subtraction signs, but never by multiplication signs "A polynomial with one term is called a monomial "A polynomial with two terms is called a binomial "A polynomial with three terms is called a trinomial"

Okay, I'll give on that one. They're not the only ones who define ‘polynomial’ to include ‘monomial’. I'll adjust my usage accordingly going forward. I can do that ‘cause it's not gonna help ya in the end anyway.

Says who? What they've done is say exactly what the fuck I said, and exactly the opposite of what the fuck you said. I have no more time for you face-savin' bullshit.

"Nah; fer instance:... followed by shit about fractions

I've no idea what the fuck that's supposed to be a "fer instance" of, and I care less. It has zilch to do with anything I said.

"It therefore follows that (√(ab) - b)(√(ab) + b) is not a polynomial."

I nowhere suggested it was. I said that a polynomial factorisation yields irreducible polynomial factors. Not only is the above not a polynomial, but the individual factors are not polynomials, irreducible or otherwise. That is because you chose an invalid factorisation method. And THAT'S because you misidentified the original polynomial as a difference of two squares.

Which reminds me -- YOU never provided a link as authority for your factorisation, in spite of you demandin' them from ME. But don't bother, I know you're wrong without you tryin'. Why don't we get back to the absolute basics and have you explain how the fuck ab is a square? Since you'll inevitably bullshit about it for dozens of posts, I'll give you the easy and obvious answer: it isn't.

Yeah, good try. It's the sort of thing that gives me hope you are not mentally deficient, but merely arrogant, misguided, and with a special talent for missing the obvious.

And speaking of the obvious, explain to me why the factorisation method is called the "difference of two squares". Since you have deftly shown that every number is tautologically the square of its square root, why don't they just call it the "difference of two numbers", or even more aptly, "the factorisation of a difference"? Why did they mention squares?

"Which reminds me -- YOU never provided a link as authority for your factorisation, in spite of you demandin' them from ME"

Actually, I did, you just didn't like them, so you've conveniently forgotten. And I'll probably go back and get them again; there's one in particular that I'll probably be wanting. But, rather than look for them again now, I'll just get you a new one.

PurpleMath "When you learn to factor quadratics, there are three other formulas that they usually introduce at the same time. The first is the ‘difference of squares’ formula. "…a difference of squares is something that looks like x² – 4. That's because 4 = 2², so you really have x² – 2², a difference of squares. To factor this, do your parentheses, same as usual: "x² – 4 = (x )(x ) "You need factors of –4 that add up to zero, so use –2 and +2: x² – 4 = (x – 2)(x + 2) "(Review Factoring Quadratics, if this example didn't make sense to you.) "Note that we had x² – 2², and ended up with (x – 2) (x + 2). Differences of squares (something squared minus something else squared) always work this way:" (emphasis added)

You asked before what the hell I meant when I said it ‘always’ works. I meant pretty much the same thing they meant. Always works this way; not optional; this is how ya do it.

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯ "And speaking of the obvious, explain to me why the factorisation method is called the ‘difference of two squares’"

No, irrelevant at this point. Waste of time.

And, we're gettin’ pretty close to where I gotta go. I can't hang ‘round with you two days in a row. If ya got something big, hit it now. Else go on to your next step.

## هناك 310 تعليقات:

1 – 200 من 310 ›أحدث أحدث»one of many facets of the problem

All religions look like superstition to those who don't believe in the religion. Miracles are only miracles to believers; to the rest they're phenomena, or mere coincidence.

"

One man's religion is another man's belly laugh."R.A. Heinlein―Time Enough for Love

Zeyad ate my hamster!

Non-religion looks like superstition to the religious too. Indeed, the non-religious are most often blindsided by their irrational belief in their own objectivity.

That was the loony Catholic of course.

(Quite weird -- I accidentally hit some key while typing my name and it accepted the comment without any word verification. Can't reproduce it again. Although I notice on several occasions when I just couldn't read the word verification I got away with my best attempt, even though the chances of me having got it right on every such occasion are very low. While I'm on the subject of blog technicalities -- Zeyad, your blog's main page takes forever to load with every post going back to the beginning of last year).

one of many facets of the problem.Intolerance of any sort is a problem.

If you ever get a chance, Zeyad, and you enjoy plays, you should see Over the Tavern. It's set in 1950's America and revolves around a young boy and his family. The boy is starting to quesiton some of the things about his religion. It's meaningful and hilarious. :)

PeteS,

While I'm on the subject of blog technicalities -- Zeyad, your blog's main page takes forever to load with every post going back to the beginning of last year).I noticed that too. But I thought it was just me, or rather my computer. The one at home, which is using XP, is slower than the one at work, which is using Windows 7. I thought it might have to do with my anti-virus software.

"

Non-religion looks like superstition to the"religious too.

This suggests an inability among the religious to differentiate between agnosticism and atheism. Notwithstanding your assertion above, I suspect this inability isn't universally, or even commonly, shared among those who are religious. Perhaps you're being blinded by an irrational belief in your own perceptivity.

Lynnette,

Unfortunately, my parents poisoned my mind with syfy and horror movies from the time when we were in the UK. I only broke free from their spell as a grown up.

"This suggests an inability among the religious to differentiate between agnosticism and atheism."This suggests you're trying to be a smart arse. The religious tend to be better educated, on the whole, about systems of belief (although that's not saying much, and should be expected anyway, since they have skin in the game).

To cut to the chase, you're wrong. Atheists don't tend to be superstitious, they tend to be deluded dogmatists. They're vastly outnumbered by the superstitious agnostics.

"I noticed that too. But I thought it was just me, or rather my computer. The one at home, which is using XP, is slower than the one at work, which is using Windows 7."Yes, and IE9 is slower than Firefox on my new i5 laptop. But they're both a lot slower than they should be.

"

…the superstitious agnostics."A bait and switch goin’ down there, ‘cept I caught it.

I would not dispute that many agnostics are superstitious to a greater or lesser degree, but that observation is quantitatively different from your assertion that ‘

[n]on-religion looks like superstition to the religious."I still think you're projecting

failure to differentiate agnosticism from atheism.your(In fact, I'd almost bet you'd be agreeing by now that your initial statement was way overbroad were it anybody but me who'd called ya out on it.)"

A bait and switch goin’ down there, ‘cept I caught it."Well, didn't take long for this exchange to take a boringly familiar twist.

"that observation is quantitatively different from your assertion that ‘[n]on-religion looks like superstition to the religious.'"I'm quite aware of that. That latter statement was not made to support my original contention, merely to point out that I distinguish greatly between agnostics and atheists, to the extent that I don't consider the latter to be non-religious at all.

"I still think you're projecting your failure to differentiate agnosticism from atheism. (In fact, I'd almost bet you'd be agreeing by now that your initial statement was way overbroad were it anybody but me who'd called ya out on it.)"And I still think you're tryin' to be a smart arse. So don't go expectin' any "debate" if y'all wanna engage in yer usual pedantry.

"

I don't consider [atheism] to be non-religious at"all.

Ah yes, figured you was going there again. The notion that denial of the existance of God and the belief that all religion is either delusion or hoax is a religion of it's own. I remember your assertion from last time.

But, I've run across that one before, usually from Protestant evangelicals, but there is a Catholic version. And I have long recognize that to be a political statement rather than a religious one. Of course, the Protestant evangelicals, and your version of Catholicism

political as well as religious beliefs.areHappily, I live in a country where the Constitution keeps folks like you in check.

Rather than wait for Lee to check all that for booby traps, I'll just cut to the chase and observe that he's settin' up to claim a distinction between superstition as an accidental trait of the self-labelled non-religious, and -- as I would claim -- an almost unavoidable consequence of the abandonment of traditional world views which took a rational progressive view of human nature and the natural world.

(And yes, I even include Islam among those world views, being, as I am, increasingly impressed by the medieval Islamic scholars that I'm reading about. I was always aware of their role as a conduit for the arrival of Greek learning in medieval Europe, but I don't think I was quite aware of how advanced and progressive their own science was.

Perhaps it would be better, at least more accurate, to say: ‘

I have long recognize that to be a political statement rather than a”strictlyreligious one."The notion that denial of the existance of God and the belief that all religion is either delusion or hoax is a religion of it's own."Now who's talkin' about bait and switch? Atheism, as I'm sure you well know but I will give you the benefit of the doubt anyway, is more than the denial of the existence of God. It is the positive assertion that the "natural" world is "all there is". You may be able to see that those are different things.

"

…Atheism…is more than the denial of the"existence of God.

See the word ‘

’ in the phrase ‘and…denial of the existance of God’ and try to follow along from there. If you're gonna insist on carryin’ on, at least try to keep up.and…Perhaps it would be better, at least more accurate, too say: ‘I have long recognize that to be a political statement rather than a strictly religious one.'"Yes, it would be a great deal better and more accurate to say that. I'm glad you rethought it.

"Of course, the Protestant evangelicals, and your version of Catholicism are political as well as religious beliefs. Happily, I live in a country where the Constitution keeps folks like you in check."Happily, I live in a country where the US constitution can be read objectively, and not through the lens of overly zealous evangelicals or "liberals". Your constitution says nothing whatever about keeping Protestants, Catholics, or anyone else in check. It grants them the same rights to hold whatever political views they damn well like, same as anyone else. I'll put your misinterpretation of its anti-establishment clauses down to a temporary rattiness borne of yer anti-religious enthuiasm.

"See the word ‘and’ in the phrase ‘…denial of the existance of God and…’ and try to follow along from there. If you're gonna insist on carryin’ on, at least try to keep up."Didn't want to embarrass you further, but if you insist ....

"

..."andthebeliefthat all religion is either delusion or hoax is a religion of it's ownSo, by your own words, atheism is a

belief. Good. Now keep up here ... do you think it is anevidence-based beliefor something else? If the former, what evidence do you think it's based on? (And just to keep you focussed, remember we are talking about a positive assertion here, so don't bother with any namby-pamby retorts about LACK of evidence or balance of probabilities)."

Your constitution says nothing whatever about"keeping Protestants, Catholics, or anyone else in

check.

No, it does not use that language. But it serves the intended purpose quite nicely nonetheless. There is much to be said for how well written it was. Got a lot done in only three pages.

"

Now keep up here ... do you think [atheism] is an"evidence-based belief or something else?

I'd have to think that would depend on the atheist. I don't suppose they all come to their conclusions the same way.

Although, strictly speaking

atheismrefers only to the disbelief in God, or gods. If there are any who don't also eschew religion they're rare."I'd have to think that would depend on the atheist. I don't suppose they all come to their conclusions the same way."I can see you have no intention of answering the question. But I'll try one more time: do you think

anyatheists' atheism is evidence-based, and what do you suppose that evidence is?While Lee lets the sniffer dogs loose on that last one, a quick chance for me to remark on the role of Iraq in the history of mathematics, which I've also been reading up on. There's a newish (2008) book that I'd like to read sometime: "Mathematics in Ancient Iraq: A Social History". From the earliest Sumerian scribblings, to the medieval Islamic period, Iraq has been at the centre of things mathematical. And while we've got some papyri from ancient Egypt showing mathematical development there, Babylonian baked clay tablets were much more robust as records and exist today in much greater number. Babylonia probably contributed as much if not more than Egypt to later Hellenistic maths. Some day I'll find more time to read up on it.

"

But I'll try one more time: do you think any"atheists' atheism is evidence-based, and what do you

suppose that evidence is?

I'm sorry, but it has never occurred to me to delve into the reasons for an atheist's denial of the existance of God

(or gods). It never interested me and then there was the overarching logical problem of attempting proof of a negative.In fact, I recall, whilst checking the Heinlein quote for accuracy this morning, that I skimmed across a Google entry that said something about proving that there was no god, something about having 50 proofs, or something like that, and I recall thinking at the time that they obviously needed a lesson in basic logic. But it never occurred to me to examine the web site behind the Google entry.

So, no. I have no intention of answering the question you posed. I don't happen to have an answer handy, and I've never been interested in the subject--still ain't. So, I'm not gonna go lookin’ for one.

So let me just get this straight. You said:

"The notion that denial of the existance of God and the belief that all religion is either delusion or hoax is a religion of it's own. I remember your assertion from last time. But, I've run across that one before... [a]nd I have long recognize (sic) that to be a political statement rather than a religious one."You are now sayin' you don't know jack shit about the topic? Indeed, that you not only don't know but don't care to be informed? Ok, figures. I guess we won't be movin' on to the topic of agnosticism and superstition then.

"

You are now sayin' you don't know jack shit"about the topic?

No, not what I'm saying. Rather, anybody who claims to have compelling evidence or actual proof of the negative, i.e. that there is no God

(or gods)has obviously made a fundamental logical error; either in the chain of logic, or in the premises.If they happen to be right, it's obviously by accident. So why should I be interested in their claims to evidence or proof?

Be like watchin’

Brunotryin’ to do his occasional elephant jumps. Ain't worth wastin’ time on.You're obviously willing to argue what you know to be loser of an argument, just for the sake of having the argument. Seen ya do it too many times not to have figured that much out. But, I am not so inclined.

Up to you whether or not you move on to agnostics and superstitions. But, I'm inclined to bet that if you cannot confuse the two classes startin’ out

(atheists and agnostics)you'll not want to deal with the second class at all. I figure this whole thing was predicated for you on being able to blur the line and slide a flauwed argument in behind the blurr. If that's not gonna work, you'll be losin’ interest real quick.(You'll go out with a bunch of bluster, of course, but you'll be headin’ out sure ‘nuff.)‘

Flawed argument’, not supposed to be a ‘’ in there.uBy the way

.ZeyadNowwould probably be the time for the casual atheist to mention Occam's razor.So Lee's decided to play stupid again. I guess it's a ploy he carries off well.

Although, you gotta admire his sheer brass neck too, accusing' me of trying' to muddy the waters with an argument HE brought up, and then, after being' too stupid to understand the explication of his own confusion, tryin' to turn the tables. Not many would be so brazen.

"

…accusing' me of trying' to muddy the waters"with an argument HE brought up…

I brought up your failure to distinguish between atheism and agnosticism.

Wanna go there now? Wanna tell us how agnosticism is religion?

I'm bettin’ agin that. Bettin’ on you givin’ us more bluster instead.

Morning has broken, and no further sign of the Catholic theocracy raising it's hoary head again…

Perhaps time for a summary, for those who've been trying to follow our little exchange.

The American fundamentalist Christian evangelical

(Protestant variety)has been developing an argument in recent years to the effect that our Constitutional right to freedom of religion doesnotinclude the right to be free of religion. I.e: Freedomreligion does not include the right to freedomofreligion. In service of this fundy political theory they've been trying to promote the argument that secularism, an absence of religion, is properly to be seen as a religion in and of itself.fromThey think this will reduce the claim to a right to be free of government promotion of religion to the status of a

competingreligion and give them a political advantage they do not currently enjoy in e.g the arguments over whether ‘creationism’ should be taught in science classes in the public schools as a credible alternative to the theory of evolution and stuff like that.Catholic fundies like

Petesalso see a potential opening for their theocratic agenda if they can sell the idea that secularism is religion. They figure they can reduce the right to be free of religion to the status of a competing religion, and thus ‘level the playing field’ as they see it.I was not cooperating with

Petesin his attempt to re-classify a position of no religious preferences to the status of a competing religion, with no protections not enjoyed by his own religion. In effect, he wants to ‘demote’ secularism to what he feels is the disadvantaged status of a competing religion. There is a political agenda behind this which the reader can probably figure out for themselves at this point. But, I was not cooperating in the required blurring of the lines that's a necessary first step in developing his argument.So he sorta blustered a bit and then seems to have faded away.

More re: American politics:

But this time economics, not religion.

"

In a speech Tuesday, [John] Boehner (leader of"the House Republicans) said that ‘allowing America

to default,’ while not such a hot idea, would be better

than raising the debt ceiling without ‘dramatic steps

to reduce spending.’ Added Boehner: ‘We shouldn’t

dread the debt limit. We should welcome it. It’s an

action-forcing event in a town that has become

infamous for inaction.’

WaPoThose clowns are gonna do it again; they didn't learn anything from last time.

LMFAO. Only Lee could be egotistical enough to take his own misguided suspicions and suggestion from 2:23 PM above, mix in a few political fantasies and attribute them to me, construct his own monologue based thereon, and declare himself 'the winner'. Lee-world must be such a fun place.

So, ya got nothin’ ‘bout agnostics and superstitions then?

I got plenty 'bout it. Would be happy to expound it too, 'ceptin' I know you are gonna vanish up yer own ass to soliloquise, then emerge back into the light to announce that even though you know jack shit about it you still won the argument you just had with y'all's own self.

Ah, yes. The secret knowledge thing again. Making you again into

The Great and Wonderful Petes. We've seen this one before.Well, have fun with that.

No secrets involved. I can see how it would appear so to y'all though, 'cos even though y'all's only interested in debating' with y'all's own self, y'all may still harbour a nigglin' worry about what it is y'all is so desperate to avoid hearing'.

"

…so desperate to avoid hearing…"If you had something you thought I was ‘

desperate to avoid hearing’ I'd not be able to shut you up on the subject.This is just more of your stock

Great and Wonderful Petesstuff, like those mighty mystery maths that you never did get around to unveiling way back when…LOL. Y'all really have y'all's obfuscatory tactics down to a fine art at this stage. If only there was a way to monetise them in the real world y'all could make a livin' from it instead of trollin' this forum. You sure y'all's not some kind of failed librul politician?

Just out of interest, y'all progressed as far as basic kiddie maths yet?

Appears I struck a nerve there.

Struck a funny bone, more like. Remember how you refused to multiply out a^2 - b^2 because it proved the factorisation you had been arguin' for was poppycock? That was probably the greatest Lee C classic of all time. Jes' refused to do the sums, no sirree. Wouldn't even agree on what factorisation meant (although I never did find out if y'all was too dumb to know, or, more likely, it didn't suit y'all to know). Laugh a minute. Particularly funny in the light of yer comments here, since y'all proved that the most Jesuitical of Jesuits was alive and well and livin' in the woods of Indiana. Even the ones that wouldn't look thru Galileo's telescope would have blushed for y'all. What a hoot.

Got him wanderin’ all over the yard now, lookin’ for somethin’, anything that'll work for a weapon

Yep, ‘pears I stuck a nerve there.

Gotcha. Still not hot on the kiddie maths then.

This from the guy who promised to show us '

hundreds’ of ways to factor a binomial expression(There are a maximum of four.)And then conspicuously failed to deliver even the four.This from the guy who promised to show us '

hundreds’ of ways to factor a binomial expression.(There are a maximum of four.)And then conspicuously failed to deliver even the four.Once in awhile something's worth saying twice, even if it was accidental.

OMG. He jes' couldn't help hisself eventually. But to come back with something' so stupid and say it twice? Now that's priceless.

How 'bout we try Lee out with the simple question he point blank refused to answer last time. Maybe he's forgotten why he couldn't answer last time.

Hey Lee. What do you get when you multiply out (a - b)(a + b)? If y'all need an interweb reference it'll be under maths for 8 year olds.

Decided to give up on the factoring and go for simple multiplication did ya? You flush out fairly easy these days.

(Although, I must give ya credit for persistence in the continued hunt for a winner. You do keep chasin’ the dream.)Yep. As expected, Lee Cardinal Bellarmine won't look thru the telescope. Funny he should drag all this up jes' to embarrass hisself.

You've already done the telescope bit. You need new material; you're circlin’ back too quick. Ya got too small a circle here; need to expand your field.

(for the audience who almost certainly weren't around after the hundreds of posts last time, Lee never DID grasp that two numbers multiplied together to give a product are FACTORS of that product. Still doesn't, as can be seen from his comment above. He still thinks the only way to get factors is through his special magical formula. That's cos Lee doesn't know what factors ARE. )

Still can't believe he wants to embarrass hisself thus.

Give it a couple of months and you'll be tellin’ folks how you tore me a new one on the subject of agnostics too.

Why wait?

Indeed, let's not wait. Why don't you finish tellin’ us all about the secret hidden religiosity of the irreligious.

That's an oxymoron as you well know. However, I was polite enough to deal with atheists first when you changed the subject to that. Now you've changed the subject to 'binomial expressions' and their factorisation, so I'm gonna set you straight there too. Just need you to co-operate and answer the outstanding question and two more even simpler ones. That can't be too much to ask, can it?

"

Now you've changed the subject to 'binomial"expressions' and their factorisation, so I'm gonna set

you straight there too

No, that was you went there first. At

, supra.4:24 PM(Which sorta helps answer the question I had lurkin’ in the back of my mind about whether or not you were just makin’ up stuff as you go, or whether you'd actually adjusted your own memory, convinced yourself of the stuff you were pretending. Not that it's really important for me to know whether or not you were deceiving yourself as well as the more casual readers. It was just a passing question in the back of my head.)More to the point:

You were telling us that:

"

Non-religion looks like superstition to the"religious.

Petes @ 2:03 PM, supra

You don't need me to answer questions before you explain that. You didn't like my explanation; let's see your

To quote your very own special self, ‘

Why wait’?Typo correction: ‘

You didn't like my explanation; let's see your.’sNope. You mentioned the "mighty mystery maths" at 12:28 PM above, before I did. Well, those maths depended on an intermediate demonstration in order to lead yer simple self to the correct conclusion. That was by way of the demonstration of a mathematical fallacy, one step of which involved factorisation. You disappeared down obfuscatory rabbit holes at every opportunity, just like you are doing on this thread. Unfortunately for you, I can keep track of the thread of an argument very closely, regardless of yer wanderings. So, no, lets deal with one thing at a time. You painted yerself into such a corner with yer factorisations that you eventually just Jesuitically plain refused to perform a simple multiplication. Let's get over that hump before we accept yer

bona fidesin the current argument.Zeyad,

Unfortunately, my parents poisoned my mind with syfy and horror movies from the time when we were in the UK. I only broke free from their spell as a grown up.lol! Right, right, blame the parents. I think syfy and horror movies are standard fare for kids. I was into that too. My friends and I even tried the seance thing. We did a good job of scaring ourselves silly. :)

I've always liked plays, but saw the one I mentioned only recently. Given some of your posts it was one I thought you might enjoy.

P.S.

That's not to say I wouldn't still enjoy a good syfy or horror flick. One of the best horror books I read was "The Relic". The movie wasn't bad, but I liked the book better.

"

You mentioned the ‘mighty mystery maths’ at"12:28 PM above, before I did.

Your ‘

mighty mystery maths’ had to do with your oft repeated claim that you had some secret ‘maths’ that would explain why it was that Einstein didn't mean what he said when he said that the matter/conversion ratio was ‘independent’ of the rules of special relativity.First you were gonna uncork ‘em on us just any minute, and then you were gonna keep ‘em secret ‘cause I didn't act appropriately impressed with your threat to uncork ‘em on us. And then you switched back and forth between those poles and various positions in between several times, and never did unveil your mighty mystery maths.

(Which of course were fictional from the get-go.)But they didn't have squat to do with your failure to get your head around the factoring of a ‘

difference of squares’ binomial square expression. Nothing at all to do with that. You went there all on your own.And it's a mere fraud anyway. I flushed ya out out on the attempt to make agnosticism into superstition. You got nowhere else to go with that, so the

thing you can do now is throw up as much dust as you can and pretend you can't explain your position ‘cause it's too dusty.onlyI knew you were gonna get here, eventually, and now you're here.

Now you'e gonna bluster some more and pretend you didn't just get burned to waterline again.

And so it ends.

Atheist, Agnostic, just Maronites by another name...;)

[Lee]:

"Blah, blah, blah ... And so it ends"LOL. And that length piece of bluster explains why you won't perform a simple multiplication? And my "mystery" maths are apparently so unmysterious that you know they're unrelated to this multiplication? There's a simple way to find out, of course. But you won't go there. Why's that?

"I flushed ya out out on the attempt to make agnosticism into superstition."Nope. Ya made one patently ridiculous claim about me confusing agnosticism with atheism. When that fell flat ya brought up the mystery maths. We haven't even touched the agnosticism claim. We'll get to it right after the simple multiplication.

"

And that length piece of bluster explains why you"won't perform a simple multiplication?

Want the short version?

The '

mighty mystery maths’ had nothing to do with the argument about binomial squares nor the appropriate factoring of same. The ‘mighty mystery maths’ dealt with an entirely different subject. The subjects did not intersect nor overlap.Petesopened the subject of binomial squares and the appropriate factoring of same, and now denies that he did. That denial was an open and intentional lie. Nothing short of that. Not a misremembering; not a misunderstanding. Just a simple lie outright lie forPetesto hide behind.(Did ya follow it that timeLynnette? I could expand a little bit if that'stooshort a version.)Lee's still havin' the same difficulty followin' the argument as he always did. The connection was very simple:

1) Lee alleged that Einstein's statement of the mass energy equivalence had nothing to do with certain earlier derivations in special relativity.

2) I set out to show the dependence of the mass-energy result on the constant speed of light, but Lee couldn't follow the maths.

3) I simplified it by showing how a different logical argument depends on the validity of all the previous steps in the argument. The example was verbatim quoted from Wikipedia (although Lee didn't know that to being with).

4) Lee claimed that not only I, but Wikipedia, was wrong. He "proved" it by claiming that c(v - c) were not factors of v - v^2. He's stuck to his guns ever since.

An intelligent five year old could multiply c(v - c). Lee won't do it, cos the final nail in his coffin is a demonstration that multiplication and factorisation are the same arguments in reverse. Instead, Lee got hung up on an Interweb article talking about factors of the different of two squares, and childishly took it to be all there was to say on the subject.

That's the whole story. That's why Lee won't do the simple multiplications. That's how it's connected to the Einstein thing. That's why Lee's a dunderhead and a liar and fraud to boot. All of this is straightforward to fact check. That's why Lee has to obfuscate.

should have read: "claiming that c(v - c) were not factors of vc - c^2"

It's still a lie. And

Petesknows it's still a lie. And I know it's still a lie.And the posting timestamped

are simply embellishments on the lie.3:00 PMAnd that's how it ends.

Big surprise! It ends with Lee STILL refusing to do the simple multiplication. He probably remembers how embarrassing his factors were ... the ones that he wasted weeks insisting we're the only valid ones. He has one great talent, that's for sure. Ain't maths or philosophy though.

Now that you've doubled down on the lie, and we both still know it's a lie, and it being highly unlikely anybody else gives a damn, we can return, now without the distractions to what actually was the point before you went looking for diversions. To wit:

"You were telling us that:

"

Non-religion looks like superstition to the"religious."

Petes @ 2:03 PM, supra

"You don't need me to answer questions before you explain that. You didn't like my explanation; let's see yours."

Are you telling me you DIDN'T insist that vc - c^2 HAD to be factored as the difference of two squares, even though it's no such thing. Are you actually claiming that?

I rather doubt you're going to repent and confess. So, that conversation is pretty much over. You mistake me for someone who cares further.

You told us that:

"Non-religion looks like superstition to the religious."

Petes @ 2:03 PM, supra"

That statement looks like foolishness on its face: I'm content to leave it lookin’ like that. If you've got nothing further to say on the subject then we're pretty much done here. I'm content to leave ya there.

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Post Script:

You've been noticeably agitated for a whole day now, excitable. Since ya got flushed. It shows. A lagniappe to leavin’ ya right there.

How pathetically embarrassing.

That was just a waste of bluster.

Christ (excuse the pun) Lee actually had the answer there and proceeded to mess it up. He's an embarrasment.

@ PeteS

A pure atheist cannot claim to base his system of belief on 'proof' since as Lee noted, he'd have to engage in the ultimate proving of a negative ... ie, proving that there is no God. Clearly that's impossible.

What is possible however, is examining what OTHERS have claimed as being

proof for Godand discardingthosepossibilities. Frankly the Bible itself was what turned me into an atheist agnostic.Naturally, I too cannot prove God conclusively does not exist.

Also, nice post, Zeyad. :)

LOL. Everyone's favourite Jesuit has spent an awful lot of time saying how the discussion is over, and none at all addressing his embarrassing math faux pas.

Bruno, agreed (although I would say that makes you an agnostic, rather than an atheist agnostic). "Pure" atheism, as you call it, is illogical -- as illogical as scriptural literalism. Both involve wilful ignorance of the evidence. My guess is there are very few "pure" atheists. Unfortunately there are quite a lot of scriptural literalists, at least in Lee's part of the world, and I can see why people would be irate about attempts to have creationism etc. taught in schools. I would be too. On the other hand -- from where I'm coming from -- I see a lot of irrationalism on the so-called "non-religious"/agnostic side. Everything from homeopathy and quack science/medicine to syncretic mixtures of eastern "spirituality" and pop psychology. Richard Dawkins has bemoaned a rising tide of irrationalism, but in my experience most of it's coming from the agnostic, not religious, camp. Most of my religious pals (and certainly for me, for my own part) have a very scientific/rational outlook on things. I attribute it to an expectation of order in the world, based on its having been "designed".

"

…an awful lot of time saying the discussion is over,"and none at all addressing his embarrassing math

faux pas.

Petes @ 7:54 AM

I'll pass for now your foolishness regarding the imaginary ‘

math faux pas’. The point of beginning was this:"

Non-religion looks like superstition to the religious."Petes @ 2:03 PM, supra

There is nothing there that would benefit from the application of some math. If you choose to leave that hangin’ out there naked and stupid, I have no great objection.

(I wouldn't try to defend that if I were you either.)Lee's now too boring to be entertaining anymore.

I'm good with that.

PeteS, it all boils down to definitions in the end. When I say atheist agnostic I mean somebody who doesn't believe in a God, believes that on the balance of the evidence that there is no such thing ... but who also accepts the fact that it is impossible to prove the non-existence of God.

I disagree that atheists/agnostics are primarily responsible for quackery and so forth. That sort of thing in my experience is rooted more in New Age mysticism than atheist principles. Having said thus, however, the only homeopath I have encountered personally was a Christian and yes, against logic, his medicines seemed to work. Go figure.

Bruno, I agree, it comes down to the definitions. That's why I rarely use the term "atheist" myself. I prefer the term "dogmatic materialist" for someone who insists (in spite of the contrary evidence, in my view) that the material world is all there is. Apart from this piece of illogic, the dogmatic materialist is likely to reject both the mystical and the supernatural.

The agnostic is a whole other kettle of fish. Most agnostics I know are only agnostic with respect to "traditional" religion. They may be entirely embracing of the New Age (although that is such a broad church as to almost defy definition) yet still profess to be "agnostic".

Regarding your homeopath, I'd put that down to credulity on your part. Bet his stuff wasn't subjected to exhaustive double blind trials. The Christian aspect doesn't surprise me though. Many Catholic nuns (a dying breed) are reiki practitioners. I certainly wouldn't say the New Age is the

exclusivedomain of self-professed agnostics.None of that addresses the assertion that a lack of religion ‘

’ superstition to the religious, i.e:looks like"

Non-religion looks like superstition to the religious."Petes @ 2:03 PM, supra

Now that

Peteshas outclevered himself by denying his original destination for that assertion(SeePetes@ 9:01 AM, supra.), he's left with a free-standing stupidity and no place to go with it.LOL. Lee's

stillhopin' against hope he can make some statement of mine co-equal in stupidity with his monumental mathematical cock up, "jes' cos' he says so". Also seems to hopin' to muscle back in on the conversation now that Bruno has been civil enough to engage.Wrong on all counts there

Petes. You have a free standing stupidity hangin’ out there. That's the one that got you into this thread. Come the end of the thread here and you still ain't fixed it, and ya ain't gonna.Ya outclevered yourself and ya got nowhere to go with it now.

I'm just enjoying that.

Post Script:

By the way, you'll notice that the 11:21 posting was not directed to you. It was about you, not

you. You should feel free to shut the hell up just any ol’ time now.to(No, I'm not lookin’ to get back in on a conversation with you.)Woohooo! Ole Lee's gettin' mighty ratty. Thanks for the offer, but it's quite ok -- I already feel free to do whatever the hell I like.

The comment that got me into this thread was never debated, due to yer obfuscations. Coulda been interesting, but not with you obviously. So yer claims about its cleverosity look pretty lame, wouldn't ya think?

"

The comment that got me into this thread was"never debated…

Yeah, I know. I'm cool with that too. Leave it hangin’ out there as is, be fine with me. Ain't like that comment exactly makes ya look the genius ya know.

LOL. We're all happy then. Lookin' like a genius to you ain't exactly far up my list of priorities. In fact, I'd find that more than a tad disturbing.

"

Lookin' like a genius to you ain't exactly far up"my list of priorities.

Of course not. Fool that you are, you thought it was your show and that it was about you.

It isn't?

(I bet I could type random sarcastic/derogatory comments here for weeks, and Lee would jes' keep comin' back for more).

Of course not.

(That OCD thing of yours must be a real bitch for you here, now that the audience is gone.)[petes] "Regarding your homeopath, I'd put that down to credulity on your part. Bet his stuff wasn't subjected to exhaustive double blind trials."

Nope and nope. I took his little white pills and water drops and a couple of days later I was much better. That said, there's no actual

proofthat it was that medicine that did the trick ... but it was a pretty unlikely coincidence. Objectively homeopathy shouldn't work at all, since I'm well aware of the methods that are used to make the final product."

The great secret of doctors, known only to their"wives, but still hidden from the public, is that most

things get better by themselves…

Lewis Thomas―The Medusa and the Snail

Objectively, homeopathy should work at least as well as placebos, and that's a lot more than "not at all". That's why proper clinical trials are the only criterion by which we should judge if any given thing works.

"

Of course not. (That OCD thing of yours must be a real bitch for you here, now that the audience is gone.)"Oh no, the joy of OCD is that it doesn't need an audience. Anyway, until you give up tryin' to get the last word in, there's always an audience of one.

"

…there's always an audience of one."Then you'll have one more shot.

"

"Non-religion looks like superstition to the"religious.

Petes @ 2:03 PM, supra

You sure ya wanna leave that hangin’ out there lookin’ like it looks?

You could try to explain yourself instead of try to raise dust and cover.

Oh yeah, sure. Perfectly sensible and verifiably accurate statement. I'm more than happy with how it looks.

How about you? Wanna provide different factors for vc - v^2? Wanna change yer opinion on how only the "difference of two squares" method can be used? Wanna tell everyone how you concluded that vc was a square?

Wanna remind us how the Wikipedia page on Mathematical Fallacies -- which has been reviewed over 1000 times over eight years -- is wrong, and the great mathematical genius Lee C is right jes' cos' he says so? LOL.

As you know and I know you're lying about the math and factoring stuff, just makin’ up the story now as you wished it had gone down then, and as it's hardly likely anybody else gives a damn anyway…

It would seem that now's the time for you scratch that OCD itch of yours. I'm gonna let you get in the last word.

(You might want to take a few minutes to consider it and make an attempt retrieve some particle of your credibility. But, I'm pretty sure you'll blow your last shot with more posturing instead.)Although, before you get in that last shot:

"

Wikipedia page on Mathematical Fallacies"I'd remind you that there is also a Wiki page that's actually

the subject of factoring that did get it right. Neither of us have forgotten that. Although you choose to pretend.onSo you admit that you said the Wikipedia page on fallacies was wrong. This oughta be fun. I'll show you yours if you show me mine. Here's mine:

http://en.wikipedia.org/wiki/Mathematical_fallacy#All_numbers_equal_all_other_numbers

See step 4, labelled "Factor both sides". You maintained, over the course of hundreds of posts, that the right hand side factorisation was wrong, and you even provided several (different) attempted solutions.

Ok, now show us the Wikipedia page on Factorisation that says that the above step 4 is wrong. Ain't that many Wikipedia pages on factorisation, so it's not like it's a big secret. But it'll be interesting to see you refuse to provide a reference here, just like you refused to do the damning multiplication earlier.

You keep claiming I'm lying about yer laughable attempts. You can refute it by just providing the link. Seems so much easier than just stonewalling each time until the audience leaves. I mean, that's kinda embarrassing, is it not?

Just in case you wanted to use your promised last shot to do something other than trying to make sure it's

your last shot, something besides tryin’ to troll me back out into a fight you lost long ago and want to re-fight now in hopes of a better outcome…notI'll ignore the above posting just this once and give you another shot at a wrap-up…

Or, we can just look at that as what you wanted to write nce you were assured that you'd not have to face a reply.

Your choice. You want that

1:46 PMto count as the one I promised not to reply to, or you want to take another shot at a parting shot?Typo, should have read as:

"

Or, we can just look at that as what youwanted to write

once you were assured thatyou'd not have to face a reply.

So, flat out denial and stonewalling, huh. Well let's just have a little link for the record:

"And it's only that particular Wiki page that was wrong on the factoring question, the other Wiki page, the one that was actually about factoring, that one got it right" -- Lee C. 12:29 AM

So, you still maintain that Step 4 RHS was not a valid factorisation of step 3, and that you can't (a.k.a won't) multiply out the RHS of step 3 to get that of step 4. That's still yer position, chump? Or is it that you've realised that you were posting idiotic drivel for 300 posts, and have painted yerself into such a corner you can't even allow it to be mentioned anymore? Could still be educational for ya, if we followed it through to its relevance to special relativity, but I can't see ya goin' there. Too much loss of face. Oh well.

"

but I can't see ya goin' there."Feel free to go there yourself. Explain the relevance. I'll watch along with any other readers you might still have.

(Countin’ your1:46 PMas your free last shot, on account of I have to count one of them, and you neglected to choose between them yourself, so I have to do it.)So I was right, then.

LOL. You want me to provide the same explanation again, so that you -- who don't actually understand what factorisation is -- can just deny things written down in black and white? There's ignorance, and there's invincible ignorance, and then there's somethin' that afflicts you which is on a whole different level.

Firs you couldn't explain why agnosticism looks like ‘

superstition’ to you unless I first answered a lot of questions you wanted to fuss over.(Later you decided that it was self-evident and needed no explanation.)Now you claim that your misunderstanding of the standard factoring rules for binomials and how it supposedly relates to the theory of special relativity

(to which it does not in fact relate)can't be explained unless I answer a bunch of tangential questions about which Wiki page was right and which was wrong.I'm beginning to see a pattern here.

However, I'll just ignore the pattern for now. And go to the last point you tried to make.

"

Could still be educational for ya, if we followed it"through to its relevance to special relativity.

Petes @ 2:28 PM, supra

You're fuckin’ bluffin’. You got squat ‘cept bluster and bluff. You cannot figure out how to make your math riddle relevant to special relativity. Go ahead. Call me on it! Set out to administer that ‘

eduction’ you so clearly threatened. Follow through on that threat. I'll follow along. No problem there.You just got your bluff called; put or fold. Your choice.

There's a lesson here for ya

Bruno. You should quit tryin’ to bail this fool out of the messes he makes. Ths isn't the first time that you prematurely tried to prop him up as a winner only to have to watch as he came slowly unhinged.And, yes, I know I misspelt ‘

education’. Just a typo. Don't get too excited about it."You're fuckin’ bluffin’. You got squat ‘cept bluster and bluff."Well

that'snot a very polite start to your request."You cannot figure out how to make your math riddle relevant to special relativity."Not only

canI, Ihaveactually done it several times, the latest on this very thread. You don't have the mental equipment to see it, but I'mstillwillin' to lead y'all through it in baby steps, so that y'all can follow it, on the assumption that yer capable of learning it."Go ahead. Call me on it! Set out to administer that ‘eduction’ you so clearly threatened. Follow through on that threat. I'll follow along. No problem there."Ahh, but there

isa problem. Y'all have demonstrated y'all's inability to follow the argument so far. That means we have to look at y'all's problems and hangups in detail. No point me continuin' on when you are already stuck at our very first point of departure. So y'all have to answer certain questions along the way, to check y'all's understandin'. Otherwise the endeavour is pointless.If y'all is acceptin' of that approach I will happily continue. In other words, you forego yer obstinacy and paranoia and I will forego the jibes, and we will both take it in steps. Contrary to y'all's oft-voiced suspicions, I am ready, willin', and 110% able.

Obviously, the first step is gonna have to be the unpicking of y'all's misunderstanding of factorisation. No way round that. But it's y'all's chance to unpaint yerself outta that corner.

Your call.

"

I have actually done it several times, the latest on"this very thread…

In this very thead? Would that be before you first wrote that you could do that, but didn't

(2:28 PM)? Or have you an imaginary posting been wanderin’ ‘round in your head some time since then?(I get the impression that you're hopin’ somehow thatifyou make an outrageous enough claim somewhere along the line then I'm going to get angry or emotional, or something, and that's what you're really shootin’ for, just to know you got under my skin is the best you're hopin’ for now. On the other hand, there's an outside chance you're just losin’ your grip on reality, but that'd not be my first guess.)I called your bluff; put ‘em on the table or don't. Your choice. You don't get to negotiate for terms after your bluff has been called; that ain't how it's gonna play.

Show or fold. Remains your choice.

Where is this bluff that you are supposedly callin' me on? I said, and I quote: "Could still be educational for ya, if we followed it through to its relevance to special relativity, but I can't see ya goin' there. Too much loss of face."

Followin' it through means goin' through it step by step so y'all are able to follow it. If y'all think I am bluffin' then call the

actualbluff, not one of y'all's imaginin'. Had too much of you backtrackin' on the original thread, when you agreed with somethin' but then suddenly didn't when y'all realised yer own self-contradiction. Ain't interested in that approach. If y'all think that's a bluff, there's an exceedingly simple way to find out."

Followin' it through means goin' through it step by"step…

Proceed in whatever manner you choose. I'll try to not interrupt your progress unnecessarily.

scroll scroll scroll ... I see Pinkie and The Brain are still at it ;)

Ok. We'll start with the factors of ab - b².

What are they?

lol!

Zeyad will have you buried down at the end of the page with posts eventually. ;)

Re:

Petesposting @8:49 AMI know I promised to not interrupt you unnecessarily. But, it may be necessary here. Tthat seems a most curious place to stop. Have reached the end of your step one?

Yep.

[Lynnette]: "

Zeyad will have you buried down at the end of the page with posts eventually. ;)"... assuming he doesn't delete the entire conversation ;-)

Well, then… You're nowhere close to demonstrating the relevance of your little math trick to the Theory of Special Relativity. You have a long way to go.

I suspect you've stopped there in hopes of taking off onto a tangential argument, and I'm not interested in having a tangential argument.

But, I follow you so far. It's been easy so far, ‘cause you haven't actually gone anywhere as of yet. But, there's still time:

"

Feel free to go there yourself. Explain the relevance."I'll watch along with any other readers you might still

have.

Lee C. @ 2:39 PM, supra

"

Set out to administer that ‘educ[a]tion’ you so"clearly threatened. Follow through on that threat. I'll

follow along.

Lee C. @ 4:18 PM, supra

So, I'm following along so far. You may proceed ahead on whenever you're ready.

(Or, I suppose, you may squat there instead, if that's what you choose to do.)"

Well, then… You're nowhere close to demonstrating the relevance of your little math trick to the Theory of Special Relativity. You have a long way to go."That, of course, is pure supposition on your part. You don't know whether I am close or not. Remember the "mighty mystery maths"? If they are a mystery, as you claim, then by definition you don't know if I'm close to a demonstration yet or not.

That said, a demonstration can only be such if it is clear to the audience (i.e. you). We've already established that yer lack of mathematical understanding prevents you from reasoning this out for yerself -- otherwise no demonstration from me would be necessary. It's partly clear to me, being as my maths is superior to yours, where your misunderstandings lie. But to be sure we cover all your educational needs, it will be necessary for you to show your evolving understanding at various points along the way.

That's why step one ended with a question for you to answer. If I provided the answer, then there seems little doubt that you would say the same as you said last time, to wit: "that's just wrong". If you wish to progress, your answer is required so that we can explore how your answer is incomplete and/or wrong, on the way to painting the bigger picture.

Pete: "Ok. We'll start with the factors of ab - b². What are they?"

Uh, I never did follow ya'lls relativity theory debate but the answer to that question would be a and b, right?

My math skills are so-so. Way above average but nowhere near those that "get it". I did struggle through the first year of civil engeneering with the math courses: linear algebra, analysis in one variable and analysis in several variables (never managed to complete the last one with a passing grade), then I flunked out and got into basic computer sience which was way easier. I get the feeling Pete has maths knowledge on par with a civil engineer graduate, and knowing how hard that is I'm not gonna get into a pissing contest with him in these matters. But the stuff you've discussed in this thread seems like pretty straight forward algebra, so far.

"

a and b, right?"Not quite,

Marcus, although your choice is understandable. The factors areand(√(ab) + b). Factored down it reads(√(ab) - b)×(√(ab) + b)(√(ab) - b)Post Script:

is the square root sign.√No Marcus, factors are numbers which when multiplied together yield a product. The product of a and b, i.e. a × b, is ab, not (ab - b²). Any numbers which multiplied together give the desired product are factors. That's the definition* of a factor.

* It's usually stipulated also that (a,b ϵ ℤ), but we will come to that additional qualification in due course.

"

It's usually stipulated also that (a,b ϵ ℤ),"I can't read that.

Marcus, can you read the final two symbols? All I'm getting are squares. Apparently I don't have the necessary font.Ah. Ok, so we have Lee's answer:

(√(ab) + b) × (√(ab) - b)

Very good. Now, step 2:

Are these the

onlyfactors of ab - b²? Well clearly they are not, since I can easily generate any number of factors I like from the one above, e.g.:(2(√(ab)) + 2b) × (½(√(ab)) - ½b)

Let us constrain the answers a bit. Suppose a and b are whole numbers, whether positive, negative or zero. In other words, they are integers, which we denote by (a,b ϵ ℤ). What are the whole number (i.e. integer) factors of ab - b², if any? Are the following still factors?:

(√(ab) + b) × (√(ab) - b)

For (a,b ϵ ℤ), read:

(a,b E Z)

The E is an epsilon, denoting "element of". The Z is normally written as "blackboard Z" or "double-struck capital Z", denoting "the set of all integers".

In other words, a and b are integers.

[PeteS]

... assuming he doesn't delete the entire conversation ;-)lol!

Well, he let us go on and on before so he might not really care. And it's a pretty innocuous argument in an old comments section. Besides it looks a little empty without comments.

I haven't checked to see if he's managed to copy back any of the old comments sections that went missing with the changes.

"

In other words, a and b are integers."andaare variables.bare integers: […-3, -2, -2, 0, 1, 2, 3…]TheseTypo:

are integers: […-3, -2,These-1, 0, 1, 2, 3…]And

are Epsilonsthese.Ε ε(I got those.)Ok, looks like we have a fundamental gap in your understanding to be bridged.

Do the variables a and b represent anything in particular? Suppose I said that a represented an avocado, and b represented a banana. Would the following statement make any sense?:

The factors of ab - b² are (√(ab) + b) × (√(ab) - b).

I'm not sure what the product of an avocado and a banana would be, let alone their square root. Instead, a and b must be certain classes of things for which those mathematical operations are defined. Since you have already given us the factorisation, what classes of things did you have in mind for a and b? (They can't be just any old thing, since we can see it doesn't work for avocados and bananas). They must represent some class of thing for which the operations you used are defined. So what is that?

"

Do the variables a and b represent anything in"particular?

Google up

Math variable definitionFirst entry""

A symbol for a number we don't know yet.""

variable- is a letter that represents an unknown"number

I believe we may safely exclude avacados and bananas from consideration. This sort of silliness is why I generally decline to answer intermediate questions for you.

(One may assumeMarcuswas generally seeking enlightment and not playing games--which is why I stopped to answerhisquestion. Obviously, the same assmption cannot be made concerning you.)Do you suppose you can proceed without further farce?

"And these are Epsilons Ε ε. (I got those.)"The "element of" symbol is a

lunate lowercase epsilon, Unicode U+03f5. Your "normal" lowercase epsilon is Unicode U+0395.Well, I'll try again…

"

Do the variables a and b represent anything in"particular?

Google up

Math variable definitionFirst entry""

A symbol for a number we don't know yet."Second entry"

variable- is a letter that represents an unknown"number

I believe we may safely exclude avacados and bananas from consideration. This sort of silliness is why I generally decline to stop and answer questions for you.

Do you suppose you can proceed without further farçe?

"

Do you suppose you can proceed without further farce?"With your co-operation, yes. Let's look at your statements:

a and b are variables.These are integers: […-3, -2, -2, 0, 1, 2, 3…]

...

[A variable is a] symbol for a number we don't know yet.

Hopefully you will notice that the things you listed as integers are numbers. A variable is -- as you pointed out -- a symbol for a number. It is possible that the number is an integer. Then we would refer to is as an integer variable. Maybe you didn't realise all of this until you Googled those definitions. Or maybe your comment at 1:35 PM was itself a farcical attempt to suggest that something could not be both a variable

andan integer*. Either way, equipped with your new understanding, revisit my statements and questions of 1:14 PM.(* That is, to be precise, a variable

representingan integer; it is more usual to simply say that the variableisan integer)."

…revisit my statements and questions of 1:14 PM."I'm already up to speed. If I need to revisit something

will letIknow.youVery good. Since you are keeping up, you will have noticed that there are two questions directed at

you:Assuming that a and b are integers, what are the integer factors of ab - b², if any? Are the following still factors?:

(√(ab) + b) × (√(ab) - b)

I'm following so far; you may proceed.

Oh… Yeah…

Jjust so you don't think I'm sandbagging you

(I did consider it), you should consider this:Definition

Prime number"

Prime Number - A whole number greater than 1"which has exactly two factors, 1 and itself.

It therefore follows, regarding your earlier assertion that:

"

I can easily generate any number of factors I like"from the one above, e.g.:

(2(√(ab)) + 2b) × (½(√(ab)) - ½b)

Happens that is

correct.notAnd how does the incorrectness of my statement follow from your definition of a prime number? (I am not sandbagging either -- I believe your statement is evidence of another gap in your understanding).

Explaining it gets me into jargon I can barely remember and may use incorrectly and then I'll have to listen to your bullshit about how knowing the jargon means ya got the concept covered, and I've had enough of that long time ago. Let's go at it another way then:

(I hope I don't discover that I should have gotten a pencil and paper for this.)Numbers

than the number being factored aregreaterfactors of that number.notExamples of proper factoring

(intergers here; it makes a difference sometimes, but not here); Google Math factor definitionFirst exampleSecond example

Third example

You will notice that

of the examples have factors of absolue valuenonethe number being factored. I.e: 24 is not a factor of 12 even though 24 × ½ = 12greater thanAssuming then

where(ab - b²)= 1 anda= 7b= (2√7 + 14) × (2√7 - 3.5).(2(√(ab)) + 2b) × (½(√(ab)) - ½b)2√7 × 2.65 so you'd be finding factors of the original

approximating 16.65 × <-.85>(ab - b²)And that's not how it works. 16.65 × -.85 ≈ -14.16; nowhere near 7.

Saw a typo though:

would be 42, not 7, and still not anywhere near -14.16(ab - b²)-42 ‼

Ah, wait… I went to close down the extra windows and noticed a definition that sheds light on the subject

Proper factors

"

The positive factors of a number that are less"than the number itself.

You are finding factors that are greater than ‘

the number itself’. This is not proper factoring.You have a trivial error there. Where you wrote:

(2√7 + 14) × (2√7 - 3.5)

should be:

(2√7 + 14) × (½√7 - 3.5)

You will find that it does, indeed, work out to the right answer of -42.

While you mull over that, I will accept your restriction that the factors must not be greater than the number being factored. Give me a moment and I will generate you an infinite number of factors that obey that restriction. Meanwhile you can redo your sums and, if you like, get back to me about why your definition of a prime proves me wrong.

"Ah, wait… I went to close down the extra windows and noticed a definition that sheds light on the subject ... Proper factors"Ok, thank God for that. That was going to be by next point. There is not just one type of factorisation. For example:

Proper factorisation -- factoring a number into its positive factors

Prime factorisation -- factoring an integer into its (unique) prime factors

Integer factorisation -- factoring an integer into its integer factors

Rational and real factorisation -- similar to integer factorisation for rational and real numbers respectively.

And so on....

Just a note of caution -- when you pluck definitions from the web, there will often be assumptions about the classes of numbers involved. We will come back to this, but to take one of your examples from earlier:

"Prime Number - A whole number greater than 1 which has exactly two factors, 1 and itself."Well, that's not right is it? I know 3 is a prime, but it has factors 1 x 3 and -1 x -3. So the definition was incomplete because it failed to say that it has exactly two factors which are Natural numbers.

This lack of attention to classes of numbers is at the root of one of your problems.

I promised you an infinite number of factors les than the number being factored. Here you are:

(ab - b²) = (n(√(ab)) + nb) × ((√(ab))/n - b/n)

where n < (ab - b²)/(√(ab) + nb)

There is an infinite number of values for n.

"

(2√7 + 14) × (½√7 - 3.5)"You will find that it does, indeed, work out to the right

answer of -42.

Damn; one of these days I'm gonna learn to not be doin’ that stuff in my head.

However; seems we do agree that there are different rules for different types of factoring, or at least that there are different types of factoring. I think that's sufficient for now.

So, what's your next step?

Typo, should read:

where n < (ab - b²)/(√(ab) + b)

(second n omitted).

However, all of this is wandering quite far off topic. If you like, I will explain your very original misunderstanding about factorisation. Alternatively we can work through these various sub-topics if it ultimately helps your understanding. If you like I will explain why it is trivial to generate an infinite number of non-integer factors of any number, rather than give you the complicated looking equation in the previous comment.

Ok, before we move on, let's just address your comment of 2:45 PM. Do you still maintain that the definition of a prime number somehow invalidates my statement? If so, how?

Also, can you answer my questions about integer factorisation at 2:32 PM?

Can't help this little aside, though:

"Damn; one of these days I'm gonna learn to not be doin’ that stuff in my head."If you were able to look at this the right way, you wouldn'a had to work it out in your head

oron paper. You wouldn'a had to work it out at all! You would've been able to see that it was trueby definition. Might get ya to that point yet.I see you've added a

to your theory. Just noticed that in passing.n < (ab - b²)/(√(ab) + b)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

"

[C]an you answer my questions about integer"factorisation at 2:32 PM?

I think so. The questions were:

"

what are the integer factors of ab - b²"Answer: none

"

Are the following still factors?:

, and ‘an interger’(√(ab) + b) × (√(ab) - b)

Of

? Yes.(ab - b²)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

"

You would've been able to see that it was true by"definition.

If you were that good you wouldn't be applying the wrong definitions.

"

Proper factorisation -- factoring a number into its"positive factors

Prime factorisation -- factoring an integer into its

(unique) prime factors

Integer factorisation -- factoring an integer into its

integer factors

Rational and real factorisation -- similar to integer

factorisation for rational and real numbers

respectively.

I see factoring definitions for ‘a number’ (twice--first and last)

(the two in the middle)).is neither an integer nor a number; it is a polynomial expression, specifically a binomial expression(ab - b²)I see you've added a n < (ab - b²)/(√(ab) + b) to your theory. Just noticed that in passing.Yes, that's perfectly allowable. All I was offering was an infinite number of factors, based on your factors of (ab - b²). My factors are based on multiplying your factors by n and 1/n respectively. I also happen to be saying that "n < (ab - b²)/(√(ab) + b)". Does that cause you a problem? There are still an infinite number of values of n, and therefore still an infinite number of factors.

I can simplify this for you, if you like:

Suppose we have two numbers m and n. Then m and n are factors of the product mn (obviously):

mn = m x n

Equally obviously:

mn = m x n x 1 = m x n x q/q

... where q is any other number.

Therefore:

qm x n/q = mn (by the associativity of multiplication, which I will explain if you don't get it)

... and there are an infinite number of possible values for q. If you want to ensure that none of the factors is bigger than the product mn, then just constrain q to be less than n. There is still an infinite number of values*.

That's all I did with your factors of (ab - b²). Your factors were themselves sums, so it looks a little more complex, but it's the same thing.

* Note that q is not necessarily an integer and therefore neither are the factors. If m,n and q are constrained to be integers, there is not an infinite number of values of q. There may be zero, but

not necessarily so, a point which will be important later on."I think so. The questions were: "what are the integer factors of ab - b²". Answer: none"Ok. Here we have to check your understanding of the meaning of algebra. You do realise that when you say that there are no integer factors of (ab - b²), that you are saying, for ANY POSSIBLE values of a and b, the quantity represented by (ab - b²) has no integer factors? It doesn't just mean that you haven't managed to find a formula on the internet that easily gives them to you.

For instance, let a = 10 and b = 8. Then (ab - b²) = 16, which definitely DOES have integer factors. Do you perceive an incongruity between this fact and your statement about the lack of integer factors. (I am not being a smartass here).

"

I can simplify this for you, if you like:"I'd love to simply things. This is as good a time as any.

Who besides you thinks that there are ‘

an infinite number of factors" for a binomial expression?"I see factoring definitions for ‘a number’ (twice--first and last), and ‘an interger’ (the two in the middle))."Correct. The definitions overlap. For example, prime factorisation IS integer factorisation, but not vice versa. The integer factors of 12 are 1,2,3,4,6 and 12. The prime factors of 12 are 2 and 3, which happen to be also integer factors. There is no anomaly here.

"(ab - b²) is neither an integer nor a number; it is a polynomial expression, specifically a binomial expression"This, I am afraid, is something you will have to get over (unless you are being intentionally obtuse). If b represents an integer, it is perfectly common parlance to say that b

isan integer. If a and b both represent integers, then (ab - b²) also represents an integer. In common (and I mean common in formal mathematics) parlance, (ab - b²)isan integer.And we've come to where you make your mistake:

"

For instance, let a = 10 and b = 8. Then (ab - b²)"= 16, which definitely DOES have integer factors.

16 is an interger, and a number, and does indeed have integer factors.

is neither an integer nor a number and has no integer factors.(ab - b²)"

In common (and I mean common in formal"mathematics) parlance, (ab - b²) is an integer.

And again, who besides your own deluded self believes that? I wanna see a link.

(I may be a little rusty on my arithmetic, but I ain't dumb enough to buy this one.)"Who besides you thinks that there are ‘an infinite number of factors" for a binomial expression?"I'd imagine that question implies that you have given up trying to follow the maths. You're about to resort to an appeal to authority, by citing internet references. I'm trying to explain to you why your internet references include some hidden assumptions that you didn't know about. If you follow the argument, you will come to understand them. If you resort to just citing references that you don't know enough to properly understand, well then you're gonna just look stupid (to everyone but yourself, perhaps).

However, even if you can't follow the argument, you can at least perform your own sanity check. If you at least understand the valid use of algebra, you can take the example of the binomial that we have been using, feed in values for a and b, and observe that there are indeed an infinite number of (not necessarily integer) factors. You can also observe that for some values of a and b, there are also integer factors, a fact you denied. That, at least, should give you pause for thought.

"In common (and I mean common in formal mathematics) parlance, (ab - b²) is an integer."

And again, who besides your own deluded self believes that? I wanna see a link."

Let's first use my

entirequote in context:"If a and b both represent integers, then (ab - b²) also represents an integer. In common (and I mean common in formal mathematics) parlance, (ab - b²) is an integer."I truly hope you are not asking for proof of that. The product of two integers is an integer. The square of an integer is an integer. The difference of two integers is an integer. Surely, you accept those facts and can combine them to see the truth of the above statement? If not, I fear for your ability to understand any of this.

"

I'd imagine that question implies that you have"given up trying to follow the maths.

Think again then. I was challenging your mis-definitions and your applicati0on of the wrong rules based on those misdefinitions.

"

There is no anomaly here."It's not a question of an anomaly. It's about you trying to apply the wrong rules--you're trying to factor a polynomial expression as if it were a known number, real, rational, or integral. It's not a number it's a polynomial expression..

"

If a and b both represent integers, then (ab - b²)"also represents an integer.

Rather

represents a formula, a calculation that can be(ab - b²)to get an integer.solveddoes not represent an integer--it is a formulaic represention of a calculation, as yet unsolved. After it's solved,(ab - b²)you have the integer.thenI.E: ((8×10) - 10²) is formula, it is not an integer.

are integers […-2, -1, 0, 1, 2,…]TheseCan you not see the difference?

"

I.E: ((8×10) - 10²) is formula, it is not an intege"Or, maybe it's a calculation, seeing as it has no variables. I'd have to look that one up. In any case, it is not an integer.

are integers […-3, -2, -1, 0, 1, 2, 3,…]. I don't have to look that one up.TheseCan you not see the difference?

And, just to repeat it for emphasis,

andaarebintegers. They are variables.notAnd

Peteshas quit his furious posting. One can only suspect that he's off googling furiously in place of the posting furiously.I'm gonna get back to the real world for awhile then. Got things to do.

But, never fear

Marcus, Ireturn. May be morning before I get back though.shall"you're trying to factor a polynomial expression as if it were a known number, real, rational, or integral. It's not a number it's a polynomial expression"Here, and in the subsequent three comments, lie the root of all your lack of understanding.

Algebra is about the symbolic manipulation of numbers. Anything that we say about a variable, we are also saying about the number that it represents. If it is an unknown, then anything we say about the unknown, we are saying about all the possible values it could represent. That is the whole value of algebra -- that we can make generalised statements about unknowns. That is why we can interchangeably say an expression

representsa number and an expressionisa number. Anything we say about the expression is true of the number it represents. If b represents the number 8 then b is an integer because 8 is an integer and the polynomial (b + 3) is also an integer because 8 + 3 is an expression representing an integer. Let's suppose we don't know what b represents, except that it is an integer. Then b^2 is an integer, because all integers squared yield integers. Lets suppose that we only know that b is a number. We still know that b^2 is a number, because all numbers squared are numbers. If b is a banana, then we are out of luck because algebra doesn't deal with bananas.Let's look at your own example. You were able to come up with two polynomials which were factors of another polynomial, without knowing or caring about the values of the variables involved.

But how do we know the statement you made was true? You followed some rule you found on the internet. How do we know

that'strue? Let's ignore that just for now, and instead ask a much simpler question: "how might we know that your statement is false?"Well, I think you would accept that I could disprove your statement as follows:

1) Choose any values of a and b

2) Calculate the correponding values of the factor polynomials

3) Calculate the corresponding value of the product polynomial

4) Multiply the calculated values of the factor polynomials and compare to the calculated value of the product polynomial

5) If they are not equal, your statement is false.

You used this exact numerical approach yourself to try to falsify

myfactorisation.In essence, your claim about your factors is that they are algebraic expressions representing numbers, and those numbers are factors of the number represented by the original polynomial.

Thus, if you claim there are no integer factors of the polynomial (ab - b²), you are making a statement that the polynomial cannot represent a number with integer factors. In fact, you only have to take

any integer values at allof a and b and your statement is immediately shown to be false.Indeed, your own factorisation method using the difference of two squares (which you have always erroneously assumed to be the only

possiblefactorisation) shows your statement to be false for any values of a and b where ab is a perfect square. Take the values 2 and 8, for instance. Your factors are both integers.And no, (having read your comment) Petes hasn't quit his furious posting. Petes is so bamboozled by how fundamental your misunderstanding is, that, in the hope of conveying the truth to you in simple terms that you might grasp, he wrote and rewrote the above several times. Not one Google result was harmed in the making of it. I'm still not expecting you're gonna get it. I think your misunderstanding is

toofundamental. You're still gonna just say "but, but, but, it's a polynomial not an integer".(cont'd)

(cont'd)

Perhaps we can try one last thing. Suppose I take the question from 2:32 PM, to wit:

Assuming that a and b are integers, what are the integer factors of ab - b², if any?.. and I rephrase it thus:

Assuming that a and b are variables representing integers, what are the factors of ab - b² which represent integers, if any?Now you do not have to get hung up on whether something is a polynomial or a number. In fact, I am asking if you can show

algebraicallythat the number represented by the polynomial (ab - b²) has factors whichrepresentintegers? By algebraically, I mean that you still deal with the variables a and b, and not with any particular values of them. You must show that there ARE integer factors, without citing any particular example. Clearly, your difference of two squares method does not guarantee integer factors because the square root of ab is not guaranteed to be an integer for all values of a and b even given that a and b are integers.This also highlights an interesting point. We know that there are

guaranteedto be integer factors of the number represented by (ab - b²) if a and b are integers (for reasons I explained earlier and can go through again if you wish). We also know that your difference of two squares method doesn't find them. That means that your approach does not find ALL the factors of (ab - b²). That on its own puts paid to your long time insistence that the difference of two squares method is the ONLY factorisation of the polynomial.Here's another one to mull over. Consider the following proof that there is an infinite number of even numbers.

1) There is an infinite number of positive whole numbers. (We're taking this as axiomatic, although we could show it using the arithmetic sequence Tn = Tn-1 + 1, but we're trying to keep things simple)

2) For any positive whole number, n, there is a corresponding number, 2n, which is evenly divisible by 2 (i.e. even).

3) Therefore there is an infinite number of even numbers.

But hang on! How can we claim that 2n is divisible by 2 (i.e even)? Only numbers are even, and using Lee logic, 2n is a polynomial, not a number! Is there some other way of proving the infinitude of even numbers that is not equivalent to this one?

I just wandered back in to turn off the computer and found a long and winding road, middle of which was this:

"

You followed some rule you found on the internet"How do we know that's true? Let's ignore that just for

now,

Okay, first of all, I didn't find it on the internet. I just looked at your calculations and saw it was wrong and saw where. I didn't have to go to the internet until I started trying to find the terminology, the jargon, to explain it.

As for how ya'll will know I was right… What more do you want than the fact that it

comes out right.always(I got more, but I can't see that I need more.)It does not lead one into errors.But the real kicker in your post was this part:

"

Let's ignore that just for now,"No. let's not.

Tell ya what ya do. You find us the rules for factoring the variable

, oraor any other variable. Put up a link.bYou won't find one. You know why? It's cause ya don't factor variables. You can factor numbers; you can factor equations, you can factor polynomial expressions. You don't factor variables!. That's the difference

(one of them anyway)between working with variables and working with numbers. So all your spin leading up to that wild ass claim that:"

…we can interchangeably say an expression"represents a number and an expression is a number

That just happens to be bullshit of the first order. We don't say that interchangeably, we can't, ‘cause it's not true. A math expression is

a number; it sure as hell ain't an integer. It may lay out how to reach a number, but it's not a number; it's at best the formula for finding a number, and that's as close as it gets.notAnd I'll be down for the evening now. Have fun lookin’ for that factoring a variable thing, trying to prove me wrong.

Post Script:

. That is a number.9That is not a number.9xHow hard can this be?

Now down for the evening.

Clearly, you've gotten bored of following the argument, and just mean to pick out random sentences to argue with. You also didn't pay too much attention to making sure you picked sentences I actually wrote. Where did I suggest you can factor a variable? If you give me the variable b, and tell me only that it represents a number, there is no rule for factoring it. That's not to say the number represented by b has no factors, only that we have no way to find them in the absence of more information. If you tell me b represents an integer, I can tell you that it has integer factors 1 and b. I can't tell you what other integer factors it might have, nor is there a rule for finding them. If you give me the expression 9x, as in your example above, and you tell me that x is an integer, than I sure as hell can tell you that 1, 3, 9, and the integer represented by x are integer factors of the number represented by the expression 9x. I can find you rules for that, but do you really want me to teach you your "three times tables"? If you tell me x represents a prime then I can tell you that the numbers I just mentioned are the ONLY integer factors of the number represented by 9x.

By the way, it's gonna get pretty tiresome if I have to keep saying "the number represented by" just to satisfy your fantasy that a variable or polynomial expression isn't a number. Also, if y'all wanna get all hardcore about definitions, there are several I have been fairly loose on in your favour so far.

Firstly, any simple variable is a polynomial. For instance, x is a polynomial of order 1, with coefficients 1 and zero. So your statement that: "You can factor numbers; you can factor equations, you can factor polynomial expressions; you don't factor variables!" is bullshit off the bat, as you would say.

Second, we have been loose with the definition of polynomial factorisation. That is defined as the process of decomposing a polynomial into irreducible polynomials. Your factorisation using the difference of two squares doesn't even produce polynomials! That's cos by the strict definition, a polynomial may only contain integer exponents. Your square roots in your factors are non-integer exponents. I was gonna explain all this to ya in gentle steps, but seein' as ya want to get all pissy, ya can go and Google the definitions to confirm I am right. Your famous difference of two squares isn't

actuallya valid polynomial factorisation at all in the case at hand! I was lettin' y'all away with it because it's not germane to the demonstration of how to do things right. If y'all would prefer that I just prove youwrong, there you have it.If ya wanna get back on track, then you better start comin' to some sort of idea of what it means to factorise anything. You are doin' the same process whether you are factorisin' numbers or polynomials. (Note for the picky: I did NOT say you do it in the same way, just that it is the same process). Furthermore, when factorisation is discussed, it MOST COMMONLY refers to integer factorisation. If you wanna be picky, then start mentioning which type of factorisation you are discussing. Your difference of two squares is a handy one for finding integer factors of a particular form of binomial when the variables involved ARE KNOWN TO BE INTEGERS. It's fuck all use for anything else. Your bastardised version of it doesn't produce integer factors, EVEN WHEN the variables are known to be integers, and, as I've pointed out, it doesn't even produce valid polynomials and is therefore not a factorisation at all.

And just to tie up the rest of yer pissy post, in case y'all hypocritically moan that I am being over-picky about the definitions. Let's relax them and accept your factorisation for a moment. You said:

"As for how ya'll will know I was right… What more do you want than the fact that it always comes out right."Two points may be made about this. First, what the fuck do you mean "it always comes out right". You mean, when I choose values for a and b, and work out the corresponding values represented by your factors, and multiply them out, they come out to the number represented by your polynomial for those values of a and b. The only reason I ever give a rats arse about an algebraic expression is because any operations I perform on it will give exactly the same results as the same operations performed on the numbers. Your distinction between the algebraic expression and the number it represents is facile and pointless. I could equally argue that the written digit two is just a symbol (which it is) and not the actual number it represents. It's ALL symbols.

Second, you may well be God Almighty, as you seem to think, but I'm prepared to bet you haven't tried your factors for the infinity of possible values for a and b. We only need a single counterexample to show you're wrong (no matter how enraged that suggestion seemed to make you). But that's no problem -- I know perfectly well how to multiply out your factors symbolically, to show that you get the right result, without having to do it for all possible values.

I also gave you an infinite number of other factors, all of which work out perfectly when you multiply them out. Apart from the fact that they weren't generated by yer beloved "difference of two squares", what's yer problem with them?

Postscript: when I say "what's yer problem with them", obviously what I mean is for you to apply your own definition of correctness, which I quote: "As for how ya'll will know I was right… What more do you want than the fact that it always comes out right."

"

Clearly, you've gotten bored of following the"argument,

What I'm getting bored with is you makin’ up stuff as you go along, just ‘cause you want it to be that way. Like this for instance:

"

Firstly, any simple variable is a polynomial. For"instance, x is a polynomial of order 1, with

coefficients 1 and zero.

That's not true.

is not a polynomial.xis not a polynomial.9xis a polynomial.(x - 1)is a polynomial.(9x - 7)(The parens, or lack thereof are not determinative.)Both are binomials.is a polynomial(9x - 7 + 7y)(a trinomial). Butorxor 1x/1 are1xpolynomials.notGoogle

definition polynomialand first rattle out of the box,First entrytells us that a polynomial is:"

An expression made with constants, variables"and exponents, which are combined using addition,

subtraction and multiplication…***

And it further tells us that

is a polynomial, but that5xy² - 3x +5y³ - 3is merely a term within the polynomial.3x(By the same token, neitherxnor1xnor9xare polynomials.)First rattle out of the box and you're wrong. And you can't get your head around the concept that you're wrong. And you think you don't need any further authority than the pontifications of

The Great and Wonderful Petesmakin’ up stuff as he goes along is all you need. Yeah, I may be getting bored with that one.So, tell ya what ya do. We'll go back to your founding error from way back when. You originally told me that you could come up with ‘

hundredsof ‘factorizations’ (Brit terminology) for a binomial square expression.(I called bullshit on ya on that at the time.)The are a maximum of four (4) ways to factor one of those, not hundreds.So, you find some authority other than

The Great and Wonderful Petesfor the proposition that one can factor a binomial square expression hundreds of different ways as if it were a number or an integer(which it is not). You find me some authority for the idea that you can factor a binomial square expressionnumber of different way ‘nwhere n < (ab - b²)/(√(ab) + b). You do that and I'll sit up and take notice.Just for what it's worth, you're confusing two concepts. You seem to think that the Lorenz transformations are a factorization of some sort. They are not. In spite of the fact that it's sometimes referred to as ‘the Lorenz factor’, it's a progression, not a factorization.

(I think progression is the right term, maybe I should look that up. Whatever, it's not a factorization at all.)Another example of you thinking that memorizing terms means you've got your head around the concepts. And it just ain't so.Oh, and just by the way… Kinda a post script kinda thing…

Second rattle out of the box and you're wrong a second time.

"

Second… *** Your square roots in your factors"are non-integer exponents

This is not true either. √(ab) is not an exponent at all, much less is it a ‘

non-integer exponent’. One would have to re-write it to get an exponent in there(of ½); i.e. √(ab) = (ab)^½., but that doesn't make the radical sign (√) into an exponent. And, even if that were not true, a ‘be that as it may’ type of thing; nobody ever said thatwas a polynomial.(√(ab) - b)(√(ab) + b)is a polynomial. But nobody ever said it's root factors were polynomials.(ab - b²)(I happen to think, off the top of my head, that's not true. For instance(6x - 3)(5x + 3)is not, strictly speaking, a polynomial I don't think. ‘Bout that time I just gave up tryin’ to parse your crap forallthe crap it contained)"First rattle out of the box and you're wrong. And you can't get your head around the concept that you're wrong. And you think you don't need any further authority than the pontifications of The Great and Wonderful Petes makin’ up stuff as he goes along is all you need. Yeah, I may be getting bored with that one."There's somethin' y'all should understand here. Y'all are not gonna "win" this argument (whatever that means) through a Googlin' competition. All you are gonna do is end up lookin'

incredibly fuckin' stupid, which is what y'all are lookin' right now. I told you that definitions tend to make assumptions and simplifications. The one about polynomials having additions and multiplications applies to the polynomial x, if you think of it as 1x + 0. Likewise, I told you (without doin' any Googlin', btw), it is a polynomial of order or degree one (because the exponent of x is 1) with coefficients 1 and 0, because there is one x and zero ones. That is not pontificatin', that is called knowin' shit. Your Googlin' disagrees? Then your Googlin' is wrong. Although it turns out that the only thing wrong is that y'all didn't read far enough. So follow that "more" link at the bottom of yer "first rattle outta the box" and y'all will find that it gives 3x as an example of a polynomial. See any additions in there, chump? A few lines later it gives 1 as an example. Any multiplications? Then follow yer "third rattle". It says "A polynomial is a monomial or the sum or difference of monomials". And it gives 9, x, and 9x as examples. Still feelin' bored now? ...or pretty fuckin' stupid?(cont'd)

(cont'd)

"So, you find some authority other than The Great and Wonderful Petes for the proposition that one can factor a binomial square expression hundreds of different ways as if it were a number or an integer (which it is not)."First thing I should point out is that the expression we are talkin' about is NOT a binomial square expression. I'm gonna let that one slide, as I have to date, on account of it is not (yet) germane to the argument, and lord knows I certainly don't need any extra examples of you lookin' pretty fuckin' stupid.

Second, I cite as my authority, the great and wonderful Lee C. Here is your definition of correctness: "As for how ya'll will know I was right… What more do you want than the fact that it always comes out right." You wanna change your own definition, go right ahead, be sure to let me know what the new definition is. Until then, I have given you a factorization. You worked it out and found it gave the right answer. Or leastways you tried to work it out and I corrected your mistakes, to show it gave the right answer. Do you now disagree it gave the right answer? (Warning: you're gonna look pretty fuckin' stupid if you do).

Then I showed you how to modify that factorization to give any number of other different ones. It did not give "n number of different way[s] ‘where n < (ab - b²)/(v(ab) + b)". That's just your misunderstanding. It used a number n, where n can have any value up to that limit, including fractional values of which there is an infinite number. Knowing that you were unlikely to understand this, I gave you a simpler example to follow. Looks like you did not bother your arse tryin'. As to me findin' a link for this -- don't be fuckin' ridiculous. I provided you a general proof. Do you think every specific example is gonna be on a Wikipedia page somewhere? Do you understand the concept of a general proof? It's kinda like when you learn that 1+1=2, and 11+1=12, you don't need a Wikipedia page for 21+1 'cos you have a rule for it. I gave you the general proof. If you'd like me to explain it again I will, seein' as you didn't get it first time round. But don't bother makin' ridiculous fuckin' demands for Googles at dawn in some internet duel.

"Just for what it's worth, you're confusing two concepts. You seem to think that the Lorenz transformations are a factorization of some sort. They are not.... etc., blah blah blah"Oh fuckin' spare me.

There's one big mistake I am sensin' I've made. That is the mistake of thinkin' that because you are prepared to argue this thing, that you have even the remotest shred of knowledge of what y'all are talkin' about. Startin' to look like y'all have an itchy Google finger an nothin' else. So we're gonna have some new rules. When you don't understand somethin', y'all can ask politely for an explanation. Throwin' out random Google hits is a waste of everyone's time, and I've had enough of that shit.

Still bored.

is(√(ab) - b)(√(ab) + b)a polynomial.not(5 - 3)(5 + 3) is

a polynomial.not(2 × 8) is

a polynomial.notI'm not particularly impressed with the argument that I should just quit lookin’ stuff up and just believe the too convenient fictions whupped up by

The Great and Wonderful Petesinstead.And seen as we had overlappin' posts, I am gonna deign to reply one more time to yer inane shit.

"

√(ab) is not an exponent at all, much less is it a ‘non-integer exponent’. One would have to re-write it to get an exponent in there (of ½); i.e. √(ab) = (ab)^½., but that doesn't make the radical sign (√) into an exponent."Your square root sign, and an exponent of one half, are the same thing. Period. For an equally stupid fuckin' example 1+(-2) does not turn the addition into a subtraction. But they are the same thing.

"And, even if that were not true, a ‘be that as it may’ type of thing; nobody ever said that (√(ab) - b)(√(ab) + b) was a polynomial. (ab - b²) is a polynomial. But nobody ever said it's root factors were polynomials."You obviously didn't follow the definition of polynomial factorisation. I suggested you Google it, but seem that you only Google your own shit. Your factors need to be irreducible polynomials. If we allow your square root shit, then there is no such as an irreducible polynomial because we can repeat your square root shit ad infinitum.

"(I happen to think, off the top of my head, that's not true. For instance (6x - 3)(5x + 3) is not, strictly speaking, a polynomial I don't think. ‘Bout that time I just gave up tryin’ to parse your crap for all the crap it contained)"Those factors are a pair of polynomials.

You are in this way over your fuckin' head. I advise going back to basics. One way or another, I will not be entertainin' anymore of this obfuscatory shite.

"Still bored."Over here we have the expression "bored stupid". That would explain it.

Although, for "bored" I am readin' it that you realised your entire "first rattle out of the box" spiel was founded on you not botherin' yer hole to read more than one sentence. That's the only explanation for how yer own Googlin' doesn't even agree with ya. I take it y'all were never serious about tryin' to understand this shit (even had you been capable). I will remember that for future reference.

"

So follow that ‘more’ link at the bottom of yer"‘first rattle outta the box’ and y'all will find that it gives

3x as an example of a polynomial. See any additions

in there, chump?

A few lines later it gives 1 as anexample.

emphasis added

I see that. And they've rather overstated the case there.

(What was it you said about folks being too loose with their definitions sometimes?)It can be re-written to be a polynomial but it isa polynomial standing by itself. They'er being too loose with application of the test for a polynomial i.e. that ‘notA polynomial is made up of terms that are only added, subtracted or multiplied.’ and they're going on to work it up even further, to cover things thatthe products of addition, subtraction, or multiplication.could beEventually they come back to reality and do notice that:

"

"Polynomialcomes form poly- (meaning ‘many’)and -nomial (in this case meaning ‘term’) ... so it

says ‘many terms’

Look at

1. How many terms do you see there?Look at

x. How many terms do you see there?¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

"

Your square root sign, and an exponent of one"half, are the same thing. Period.

Nah; fer instance:.

5 × ½ = 2½

5 × .5 = 2.5

2.5 = 2½

½ is a fraction; .5 is a decimal. A fraction is

a decimal, although they can yield the same results after all the calculations are made.notBy the same token a radical sign (√) is

an exponent, no matter how much you wish it were.notSo, getting back to the ‘

polynomial’ thing…I did a little more googling in spite of your warning that I must believe only what's told here by

The Great and Wonderful Petes’, without any further authorityAnd, you'll be happy that I did.

"

Definition of a polynomial"Before giving you the definition of a polynomial, it is

important to provide the definition of a monomial

"Definition of a monomial:

"A monomial is a variable, a real number, or a

multiplication of one or more variables and a real

number with whole-number exponents

"Examples of monomials and non-monomials

Monomials ― 9, x, 9x, 6xy, 0.60x^4y

Not monomials y - 6, x-1 or 1/x, √(x) or x1/2 6 + x,

a/x

Goes on to say that:

"

Polynomial definition:" A polynomial is a monomial or the sum or difference

of monomials. Each monomial is called a term of the

poynomial

"Important!:Terms are seperated by addition signs

and subtraction signs, but never by multiplication

signs

"A polynomial with one term is called a monomial

"A polynomial with two terms is called a binomial

"A polynomial with three terms is called a trinomial"

Okay, I'll give on that one. They're not the only ones who define ‘

polynomial’ to include ‘monomial’. I'll adjust my usage accordingly going forward. I can do that ‘cause it's not gonna help ya in the end anyway.Next thing then?

Post Script:

Be sure to notice this part.

"

Important!:Terms are seperated[sic]by

"addition signs and subtraction signs, but

neverby multiplication signs(emphasis added)

It therefore follows that

is(√(ab) - b)(√(ab) + b)a polynomial.notis(5 - 3)(5 + 3)a polynomial.notis(2 × 8)a polynomial.notI got the applications right, at least I can say that much for myself.

Post Post Script:

"

A polynomial with two terms is called a binomial."Ergo:

is a binomial.(ab -b²)"And they've rather overstated the case there."Says who? What they've done is say exactly what the fuck

Isaid, and exactly the opposite of what the fuckyousaid. I have no more time for you face-savin' bullshit."

Nah; fer instance:... followed by shit about fractionsI've no idea what the fuck that's supposed to be a "fer instance" of, and I care less. It has zilch to do with anything I said.

"It therefore follows that(√(ab) - b)(√(ab) + b) is not a polynomial."

I nowhere suggested it was. I said that a polynomial factorisation yields irreducible polynomial factors. Not only is the above not a polynomial, but the individual factors are not polynomials, irreducible or otherwise. That is because you chose an invalid factorisation method. And THAT'S because you misidentified the original polynomial as a difference of two squares.

Which reminds me -- YOU never provided a link as authority for your factorisation, in spite of you demandin' them from ME. But don't bother, I know you're wrong without you tryin'. Why don't we get back to the absolute basics and have you explain how the fuck ab is a square? Since you'll inevitably bullshit about it for dozens of posts, I'll give you the easy and obvious answer: it isn't.

Next question?

"

Why don't we get back to the absolute basics"and have you explain how the fuck ab is a square?

That's too easy.

is the square ofab√(ab)Just as 7 is the square of √7, and 3 is the square of √3.

It's called a tautology; it's true every time.

Yeah, good try. It's the sort of thing that gives me hope you are not mentally deficient, but merely arrogant, misguided, and with a special talent for missing the obvious.

And speaking of the obvious, explain to me why the factorisation method is called the "difference of two squares". Since you have deftly shown that every number is tautologically the square of its square root, why don't they just call it the "difference of two numbers", or even more aptly, "the factorisation of a difference"? Why did they mention squares?

"

Which reminds me -- YOU never provided a link"as authority for your factorisation, in spite of you

demandin' them from ME

Actually, I did, you just didn't like them, so you've conveniently forgotten. And I'll probably go back and get them again; there's one in particular that I'll probably be wanting. But, rather than look for them again now, I'll just get you a new one.

PurpleMath

"

When you learn to factor quadratics, there are"three other formulas that they usually introduce at the

same time. The first is the ‘difference of squares’

formula.

"…a difference of squares is something that looks

like x² – 4. That's because 4 = 2², so you really have

x² – 2², a difference of squares. To factor this, do your

parentheses, same as usual:

"x² – 4 = (x )(x )

"You need factors of –4 that add up to zero, so use

–2 and +2:

x² – 4 = (x – 2)(x + 2)

"(Review Factoring Quadratics, if this example didn't

make sense to you.)

"Note that we had x² – 2², and ended up with (x – 2)

(x + 2). Differences of squares (something squared

minus something else squared)

always work thisway:

(emphasis added)

You asked before what the hell I meant when I said it ‘

always’ works. I meant pretty much the same thing they meant.works this way; not optional; this is how ya do it.Always¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

"

And speaking of the obvious, explain to me why"the factorisation method is called the ‘difference of

two squares’

No, irrelevant at this point. Waste of time.

And, we're gettin’ pretty close to where I gotta go. I can't hang ‘round with you two days in a row. If ya got something big, hit it now. Else go on to your next step.

"No, irrelevant at this point. Waste of time."Irrelevant or

awkward? Have it your way. Y'ain't gonna learn by decidin' that only what ya think ya already know is relevant. Your loss.Ok, next step:

The polynomial factors of (ab -b²) are b and (a - b).

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