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