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 misunderstanding
each other. This is my claim:

Here is a list with three lines containing five natural numbers

1) 1, 2, 3, 4
2) 1, 2, 3, 4, 5
3) 1, 2, 3, 4

We 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 set
of natural numbers (including line-numbers) has a smallest element? Or
do you believe that here the exception proves the rule?

Regards, WM