```Date: Feb 1, 2013 10:12 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 203

On 1 Feb., 13:50, William Hughes <wpihug...@gmail.com> wrote:> Let a potentially infinite list, L,> of potentially infinite 0/1 sequences> have the property that every> (in the sense of "all from 1 to n")> potentially infinite 0/1 sequence> is a line of LLet us take an example to visualize your ideas:1) 0.000...2) 0.1000...3) 0.11000......n) 0.111...1000...Here the "..." does not mean actual infinity but only for every nthfigit there is a digit at position n+1.>> Let s be a potentially infinite> 0/1 sequence.0.111...>> Does this imply that there is> a natural number m, such that s> is the mth line of L>> ?In the case sketched above, every initial segment of 0.111... is in aline of the list. And in potential infinity there is not more thanevery initial segment. Nevertheless, we cannot fix a line number mwhere we could find it. An infinite list has no last line although ithas no line number that is larger than every natural (and also nonumber of lines that is larger than every natural number).Regards, WM
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