In article <slrni2gp3j.jrj.tim@soprano.little-possums.net>, Tim Little <tim@little-possums.net> wrote:
> On 2010-06-28, Owen Jacobson <angrybaldguy@gmail.com> wrote: > > So, here is an informal presentation of Cantor's diagonal argument > > that avoids the word "list" (as well as a few other common verbal > > shortcuts): > > > > 1. Let S be the set {0, 1}^N. > > 2. For any function L from N to S, we can identify an element of S not > > in the image of L. > > Peter is incapable of separating the usual informal phrase "we can..." > from his fixed idea of "there exists a finite algorithm that can...".
Note that the "anti-diagonal algorithm" which produces the anti-diagonal from a list of binary sequences is itself quite clearly finite, even though it acts on something which is not.
