Talk:Van der Waerden's theorem

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In the statement of the theorem, we use {1,...,N}, but in the proof we use {0,...,N-1}. Should we use the same convention throughout? AxelBoldt 03:59 Jan 13, 2003 (UTC)

I've incremented the numbers in the proof by 1 to make it consistent. Terry 17:58, 6 Sep 2004 (UTC)

You cannot just increment all the numbers in a proof with no understanding of what is going on; the "consistent" proof was completely wrong. For example, you had

That is, there are two integers b₁ and b₂, both in {1,...,33}, such that c(b₁·5 + k) = c(b₂·5 + k) for all k in {1,...,5}.

which makes no sense, because if b₁ is 33 then later on b₃ will be larger than 325.

I have reverted the page. Please feel free to add back the remarks you put in about upper bounds, or to revert the page again and then correct the damage you did to the proof. -- Dominus 13:40, 7 Sep 2004 (UTC)

Sorry about that. I went through the proof again; the error you pointed out was the only error I made in the proof, as far as I can tell. I'm pretty sure it's correct now. Terry 05:59, 8 Sep 2004 (UTC)

Yes, you're right. I'm sorry I said you had no understanding of what was going on; it looked to me like you had just done a global replace of each number n with n-1. Thanks for correcting the proof and adding back your remarks about the upper bounds. -- Dominus 13:39, 8 Sep 2004 (UTC)