Date: Mar 16, 2013 5:30 AM
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?