```Date: Jan 30, 2013 6:32 AM
Author: William Hughes
Subject: Re: Matheology § 203

On Jan 30, 12:21 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> On 30 Jan., 12:02, William Hughes <wpihug...@gmail.com> wrote:>> > Summary.  We have agreed that>> > For a potentially infinite list L, the> > antidiagonal of L is not a line of L.>Do you agree with the statementFor a potentially infinite list, L,of potentially infinite 0/1 sequencesthe antidiagonal of L is not a lineof L?> Yes, that is unavoidable. Up to any n, the diagonal differs from every> antry.>> But if you assume that all terminating decimals can be enumerated and> written in one list, then it is impossible that the antidiagonal> differs from all of them at finitely indexed digits, because every> finitely indexed digit belongs to a terminating decimal. And they are> all in the list by definition.>>>> > The question is:> > Does this imply>> > There is no potentially infinite list> > of potentially infinite 0/1 sequences, L,> > with the property that> > any potentially infinite 0/1 sequence, s,> > is one of the lines> > of L.>> What means "there is" with respect to potential infinity?> In my opinion potential infinity means an evolving process.> Look at thís sequence:> 1) 0.1> 2) 0.11> 3) 0.111> ...> where we can calculate ever line n. But we cannot calculate all lines,> because then we had all n, i.e., the actually infinite set |N (in the> first column). And with it we had the old problems.>> Moreover we had all natural indices in the columns without having all> indices in one line (the last one, but that is not existing). So we> have all indices in this triangle. But we know that all indices that> are in two lines, also are in one of them. By induction we can prove> that for every line, since every line has a finite number ...>> No actual infinity is untenable. And with it every "there is" with> respect to infinity.>> Regards, WM
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