```Date: Jan 30, 2013 3:28 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 203

On 30 Jan., 00:16, William Hughes <wpihug...@gmail.com> wrote:> On Jan 29, 10:11 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > On 29 Jan., 21:28, William Hughes <wpihug...@gmail.com> wrote:>> <snip>>> > > It does, however, imply that d in not one> > > of the lines of the list L>> > For that sake you must check all lines. Can you check what is not> > existing?>> So now your claim is>> We can know>>   There does not exist a natural number n>   such that d is equal to the nth line>   of L>> but we cannot know>>   d is not one of the lines of LYou are trying hard to misunderstand!For a potentially infinite set L we can know: d is not in line numbern.But a potentially infinite set is not actually infinite. And withoutactually infinite sets, you have no uncountability. For instance, allfinite subsets of |N make up a countable power set. Only the actuallyinfinite subsets make up an uncountable power set. But "actuallyinfinite" means a number larger than every n. It is easy to understandthat this number can never be exhausted by finite numbers n. Thereforewe cannot prove that d is missing in the actually infinity list from"for every n in |N, there is no line n that contains d".We will never know something for all lines as we will never be able toknow all lines, since beyond every line n there are infinitely manyfollowing.Regards, WM
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