User:Larryv/0.999.../Other discussions

This is an archive of arguments regarding the statement $$0.999\ldots=1$$. They are mostly taken from the archives of Talk:0.999.../Arguments and are "discussions" which I found especially funny. I have chosen to copy the text exactly as it appeared originally, despite formatting errors and so forth; however, I have used my own section headings for each.

THE REASON INFINITE 0.9 IS <> 1 IS BECAUSE!....... (May 2006)
THE REASON INFINITE 0.9 IS <> 1 IS BECAUSE!.......

N = 1/3 = O.33333333333...... This calculation results in an INFINITE stream of 0.3's But more important is

the fact that its a perfect Calculation! there are no numbers! or fractions of numbers left over! what I mean

by this is! if it was possible to look at the last .3 it would onlly be .3 there are no other numbers Hiding!

So now we want to find the true Value of INFINITE 0.9 Easy! N * 3 = 0.999999999......No numbers left over!

Or as below!

0.3333333333333333333333333333333....................... + 0.3333333333333333333333333333333....................... + 0.3333333333333333333333333333333....................... - 0.9999999999999999999999999999999....................... = -

A.R.B


 * So you show that 0.9999... = 3*N = 3*(1/3) = 1. While I agree (and while that proof is listed in the article as the "fraction proof"), I fail to see the point of your post, especially considering the headline. Yours, Huon 13:37, 17 May 2006 (UTC)

WRONG!!

1/3 = 0.3... + 1/3... = 0.3.... + 1/3... = 0.999999......... NOTHING LEFT OVER!

A.R.B


 * What exactly is wrong? Are you saying that 3*(1/3) is not equal to 1? Yours, Huon 13:37, 18 May 2006 (UTC)

EXACTLY! 3*(1/3) CAN ONLY EQUAL 1 IF YOU ROUND THE NUMBERS UP!

1/3 = 0.3333... THE LAST NUMBER? IF POSSIBLE MUST BE .3 SO 3 * .3 = .9 = INFINITE 0.99999 ...

A.R.B


 * I'm sorry to say so, but you seem not to understand fractions. More or less by definition, 1/3 is the number which, when multiplied by 3, gives 1. (In general, a/b is the number which, when multiplied by b, gives a.) This does not depend on rounding. Yours, Huon 14:13, 18 May 2006 (UTC)

IM SORRY TO SAY THAT WHEN YOU MUTIPLY 0.3 * 3 YOU GET 0.9

A.R.B


 * You needn't be sorry for that; I agree. But I fail to see how 0.3 (which can be written as the fraction 3/10) is related to 1/3. Surely, three thirds equal one?
 * By the way, I would ask you to sign your posts, using four tildes (~). Also, writing in all caps is usually considered equivalent to SHOUTING. Yours, Huon 14:08, 19 May 2006 (UTC)

A zillion cows (October 2006)
There are 2 planets with a zillion cows on each planet. Only cows, nothing else but grass and water for them to drink. On one planet, you vaporize .99999999% (repeating) of all the cows. On the other planet, you vaporize 100%, or all the cows. You must kill and eat the remaining cow from each planet. A ha! One will have 0 cows because you vaporized them all, the other will have at least 1 cow because you can't vaporize a partial cow. Thus 1 does not equal .9999999 (repeating). Perhaps in most mathematical equations, but not in reality, particularly when each factor is turned into a %. Or when the numbers actually stand for something. Which is, if i'm not mistaken, the point of math. In other words, you take a test, you get a .999999% and your friends get's em all right. It's not the same. You hit a gillion baseballs + 1 in a row. You friend hits a gillion but doesn't hit that last one. Not the same. You just have to think outside of your mathematical boxes, erm.. cubes. Have fun!

Note- if .999(repeating) is really = to 1, then 1.9999999 (repeating) would have to be equal to 2 etc... this is one of those polemicized math arguments made for people who like to show off, when the simplest explanation will work, the two are simply not =


 * If you vaporize only an integer number of cows, and you don't vaporize all of them, and you convert the fraction vaporized into a percent, do you really think you'll get 99.999…%? Melchoir 08:16, 25 October 2006 (UTC)


 * BTW, as discussed on this page 1.9999... does in fact equal to 2 etc. Nil Einne 19:18, 26 October 2006 (UTC)


 * If you vaporise "only" 99.999...% of the cows, you'll have no cows left, not one. (And even if you disbelieve the concept that 0.999...=1, you'd still only have an infinitesably small bit of dead cow left, which ain't much use.) --Dweller 08:46, 25 October 2006 (UTC)

Really? Unless I vaporize 100% of the cows then there will be some remaining cow left. I can't, nor do I have to define what % of the total number of cows that single cow represents but the honest answer is that 100% is not = 99.9999(repeating)% You missed my baseball analogy. Inifity + 1 is always greater than infinity.

This isn't true either, again, you either vaporize or not vaporize a cow. You don't get to choose a fraction of a cow, that's making up your own rules. Vaporize is just meant to be a means anyways, you can't kill a % of a cow. I used cows because they can adequately represent something that cannot be split into a % by someone who wishes to insert infinity in the middle.


 * Call me crazy, but I've always been of the firm belief that cows are not real numbers. Stebbins 14:08, 25 October 2006 (UTC)


 * Er infinity + 1 is greater then infinity? Do you know what infinity is? How exactly do you have something greater then infinity? If something can be greater then infinity then there is no infinity! Nil Einne 19:21, 26 October 2006 (UTC)

The cows merely represent real, whole numbers. the .999 and 1 are multipliers applied to the total sum of cows, a billion, zillion, or infinite number of cows. If the intergers are applied there will be a difference, hence they're not the same.


 * LOL @ Stebbins. As to the cow situation, the argument is flawed as soon as we realize that we are dealing with merely a zillion (in other words finite number of) cows.  It is hard for anybody to get a sense of infinity (rightly so) and in an ideal world we could break it down to simple visualizations involving farm animals.  Sadly, even the biggest number you can think of (I like to use 10 to the google factorial since it's fun to say) is nothing compared to infinity.  Thus, we must forgo our human tendency to try and rationalize (unfortunate word choice) this concept.  Either trust the proofs based on mathematics, or ask for a better explanation of their foundations.  Please do not try and explain it (or disprove it) in any real world setting; it'll make your head explode.  -bobby  14:41, 25 October 2006 (UTC)

You again, Fail to think out side the box. It's quite easy to imagine infinity, it is perhaps easier to imagine infinity than most other finite numbers. Picture 2,435,059 cows. Can't? Ok, picture infinite cows? Easier yeah? You are kidding all of us if you think your brain can get a hold of 10 to the google factorial but not infinity, I ask you what the difference is? You are still deep, buried within the box. Your mind falling back on your factorials and equations. If a simple concept like understanding that .999(repeating) is not = 1 makes your head explain you're obviously too wrapped up in preconceived mental barries.

The fact is I did explain it in a world setting. Use both numbers as multipliers on whole numbers representing finite, absolute numbers. You don't get to divide the cows, the cows represent the smallest decimal that divides .999 and 1, its a metaphor for what your mathematical lexicon can't express on paper- but I've easily proven with a rediculous example about vaporizing cows. It has to do with symbolism and representation. I also resent your directing me in not explaining this simply, and finally to you all who use this as a launching pad for needless, fruitless pride and elitism. Some mathematical concepts, like many of those in quantum physics for example can only be described with words, not with conventional mathematical symbology. I propose that this is one of those concepts. Anything less than 100% is not = 100%.


 * Nobody is arguing with that. What people are saying is that 99.9...% actually isn't less than 100%.  Your cow argument would be stronger if you had an infinite number of cows rather than a zillion.  If you have only a zillion, there is absolutely no question that vaporising 99.9...% of them will leave you with no cows at all.  If you have an infinite number of cows, then what you have left is up for debate based on the number system you are using.


 * You're completely right. I think the above editor is having a problem visualising infinity (despite his/her claims) because s/he appears to think there's something larger then infinity Nil Einne 19:24, 26 October 2006 (UTC)


 * I'd like to point out that in contexts such as cardinal numbers, there are different magnitudes of infinities. So $$\aleph_0$$ is infinite, and yet $$\aleph_1$$ is greater than it. -- Meni Rosenfeld (talk) 19:36, 26 October 2006 (UTC)


 * I know, it's another one of those things I love to baffle people with. (Although, I think baffling people with 0.999..=1 is meaner). Of course at that stage you have to be clear that you're using very specific (although reasonable) definitions of "greater than".  When will transfinite numbers or cantor diagnalisation be a featured article so we can have all this fun again?