Physics contradicts maths - how is this possible?

There is a simpler proof, in my opinion:10x-x = 9xx=0.999...therefore9.999... - 0.999... = 9xtherefore9 = 9xthereforex=1=0.999...Oh, I see Rick got there first. Nevermind...Edited by Modulous, : d'oh

I just assumed that 9/10 - 9/10 = 0 that 9/100 - 9/100 = 0 and that this continues all the way. Thus 0.999... - 0.999... = 0. These are the same assumptions that kongstad used, only presented in algebraic form which I consider simpler to understand.Hopefully you don't feel that x - x = 0 is an assumption that is not warranted do you?

Right you just proved that 2 x infinity = infinity. Irrelevant to the fact that x-x = 0 for all real numbers. Are you suggesting that π - π does not equal 0?

If it's not a real number, then it doesn't matter does it? Yes I can see that. I'm not sure how one could argue that 9/10 + 9/100 +9/1000... diverges. It wasn't meant to be mathematical equation. Replace it with English if it makes things better for you. You proved that the sum of two infinite values is itself an infinite value. I seriously doubt I am murdering that which I am not engaging in. A few lines of algebra that were provided to me via a mathematician hardly constitutes a rigorous but absurdly inaccurate mathematical analysis. Obviously, why would I argue with that? I didn't say my proof was better or more thorough. It was more simple, obviously that means less axioms are explained. The more rigorous proofs could in theory take hundreds of pages of axiom declarations - I am not going to embarrass myself or murder the subject by attempting it.

Of course it matters for the proof. It doesn't really matter in context unless Agobot is of the opinion that it does diverge. I don't see that is the case, and it seems implied that Agobot does not think they diverge. An obvious statement. Did you think that I thought it was mathematics that you needed to correct me?

We are on a debate forum, not a pure mathematics exam. I only bother to debate points that are under contention. As I said, it is possible to fill every answer with pages of axioms - but why bother if everyone already accepts them? How would that advance the debate?Further - a more complete proof had already been given, I gave an admittedly much simpler one which was obviously less complete that might help Agobot understand the point, serving a springboard to further discussion.Now, had Agobot turned around and said "But, you are assuming that the series converges", then we'd could move from there to demonstrating that it does. Baby steps, in debate, often prove more valuable than taking great leaps.

Perhaps you are yet again misunderstanding my purpose; it was to serve as a point of advancing discussion rather than piling on with mathematics that Agobot might have been ignorant of. If Agobot was able to follow kongstad's proof, then that is fine. However, it might have been over his head so I thought I'd start with something else. In some circumstances I have found it useful for springboarding discussion onto more advanced and correct matters. I find that a good way to learn is to try and argue against a certain position - but it helps if you understand the position.As wiki usefully summarises:

quote:

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The validity of the digit manipulations in the above two proofs does not have to be taken on faith or as an axiom; it can be proven by investigating the fundamental relationship between decimals and the numbers they represent. For finite decimals, this process relies only on the arithmetic of real numbers. To prove that the manipulations also work for infinite decimals, one needs the methods of real analysis.

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I guess something akin to springboarding did occur, which is good, but the original poster hasn't chimed in since the question was asked and things are devolving into needless pedantry. I don't dispute your points from a pure mathematics point of view - I just dispute the wisdom of requiring ironclad proofs for all statements in a debate setting. I eagerly await Agobot's return to see what they make of the subsequent discussion.

Yes, that might be the case, which is why I said I eagerly await any replies by Agobot to see where things go from here.