```Date: Feb 2, 2013 4:45 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 203

On 1 Feb., 22:54, William Hughes <wpihug...@gmail.com> wrote:> Previous was too complicatedThen I will skip it.>> Can a potentially infinite list> of potentially infinite 0/1> sequences have the property that>>    if s it a potentially infinite 0/1>    sequence, then s is a line of LYou have to distinguish between every and all (in the usual sense)because a potentiall infinite list is not complete.Compare the potentially infinite set (or better say sequence) ofnatural numbers as the common example.There is not a sequence of all natural numbers (because that wouldrepresent an actually infinite set).There is nothing but finite initial segments (1, ..., n). Howeverthere is no upper threshold m limiting n to n < m.This potentially infinite sequence has the properties:1) For every finite initial segment (1, ..., n) of the sequence we canfind another n+1 (or 2n or 2^n or n^n) that is not in the initialsegment.2) For every n there is a finite initial segment containing n as wellas (or 2n or 2^n or n^n).3) There is no meaningful expression starting or ending or containg"for all finite initial segments of the sequence" or "for the wholesequence" but only "for every finite initial segment of the sequence"or "for every term of the sequence".Regards, WM
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