```Date: Feb 22, 2013 6:05 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 22 Feb., 02:08, William Hughes <wpihug...@gmail.com> wrote:> So>>      A) For every natural number n, P(n) is true.>>         implies>>      B)  For any n: There does not exist a natural number>          between 1 and n such that P(n) is false>> However, we cannot conclude>>      B')  There does not exist a natural number>           m such that P(m) is falseIn potential infinity there is no actually infinite set, i.e., thereis no completed infinity. That means there are only finite sequences.However we cannot find a last element, although we can conclude thatit exists.Compare my example:     A              B--> 1         -->{ }--> 2,1      -->{ }--> 2         -->1--> 3, 2     -->1--> 3         -->1, 2--> 4, 3     -->1, 2--> 4         -->1, 2, 3...--> n         -->1, 2, 3, ..., n-1--> n+1, n -->1, 2, 3, ..., n-1--> n+1     -->1, 2, 3, ..., n-1, n...There is no last element in B. Every x from 1 to every n you desirecan be in B. Nevertheless there is never an empty A.That is all we can know about infinity. (Not my fault.)Regards, WM
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