```Date: Mar 16, 2013 5:30 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 224

On 15 Mrz., 23:27, William Hughes <wpihug...@gmail.com> wrote:> On Mar 15, 8:34 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>> > Let's first prove that already two cannot be necessary by the fact> > that two always can be replaced by one of them without changing the> > contents.>> This is true but the fact that the two lines are> necessary has nothing to do with their contents.  Two lines> cannot be replaced by one of them without changing the number> of lines.Why should line-numbers be changed? Perhaps we are misunderstandingeach other. This is my claim:Here is a list with three lines containing five natural numbers1) 1, 2, 3, 42) 1, 2, 3, 4, 53) 1, 2, 3, 4We can remove lines 1 and 3 without reducing the contents ofthe list.Line number 2 remains line number 2.> Consider the case is potential infinity.> A set of lines, K, that has an unfindable last number> must contain at least two findable lines.> The fact that these two lines are necessary has> nothing to do with the contents of the lines.Here I would like to see an example.But I would ask you in advance: Do you agree that every non-empty setof natural numbers (including line-numbers) has a smallest element? Ordo you believe that here the exception proves the rule?Regards, WM
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