Re: Relative Cardinality



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.

Regards, WM

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