Re: Relative Cardinality

In article <1120676597.351679.46340@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

> Randy Poe wrote:
> > mueck...@xxxxxxxxxxxxxxxxx wrote:
> > > As this would lead to strange results like Card(N) =
> > > Card({Primes}),
> >
> > Of course, Card(N) does equal Card(Primes).
> >
> > Does WM think there is a natural number n such that the
> > n-th prime does not exist?
>
> Yes, it is so. I am not sure, whether sequences like 111...111 with n
> 1's or like 10^2n - 10^n + 1 do ever cease to supply primes now and
> then. In principle such numbers with 10^10000 digits do exist and
> perhaps could be prime. The prime number 10^100 does not exist,
> however, for the simple reason that we cannot count up to that number
> step by step.

Counting up in cents to the U.S. national debt is impossible, so WM
declares that it does not exist?
.