# Reference for Diagonalization Trick

There is a standard trick in analysis, where one chooses a subsequence, then a subsequence of that... and wants to get an eventual subsubsequence of all of them and you take the diagonal. I've always called this the diagonalization trick.

I heard once that this is due to Cantor but haven't been able to find a reference (all searches for diagonal and Cantor lead to his argument about the uncountability of [0,1].

Does anyone have an exact reference?

Thanks.

B.

• Reed & Simon here ;-) – Francois Ziegler Apr 26 '14 at 1:54
• I wouldn't be surprised if it's only the idea of diagonalization that is due to Cantor (in his proof of uncountability of $[0,1]$) and its particular manifestation for iterated subsequences was due to someone else later. – KConrad Apr 26 '14 at 2:04
• This isn't really a "diagonalization argument" in the modern sense used by logicians, though it does share some key ideas. Rosenthal has called this type of argument "Ramsey's Theorem for Analysts", see my answer here, so it could as well be called a "Ramsey trick". – François G. Dorais May 4 '14 at 14:01