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