|
|
Re: Matheology § 210
Posted:
Feb 5, 2013 5:22 PM
|
|
On Feb 5, 10:51 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
> On 5 Feb., 21:55, William Hughes <wpihug...@gmail.com> wrote:
>
> > On Feb 5, 6:02 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>
> > <snip>
>
> > >... one cannot even put all natural numbers in
> > > correspondence with all natural numbers.
>
> > However, one can put every natural number in
> > correspondence with every natural number.
>
> One can have that by belief or decreed by the powers that be.
> n <--> n is the finite expression of this belief. But its validity is
> dubious because one cannot have possibly in a possible list that
> contains every finite initial sequence of the sequence of natural
> numbers the sequence s of every finite initial segment of the sequence
> of natural numbers.
WH: So we have potentially infinite sets like |N
WH: where you can say
WH: If L is a potentially infinite list of
WH: natural numbers then L can have the property
WH: If n is a natural number then n is a line of L
WM: or if FIS(n) is finite, then it is a line of L
|
|
