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.

ideaof 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. $\endgroup$ – KConrad Apr 26 '14 at 2:04