Re: Relative Cardinality

In article <1120742497.832998.137320@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

> Proginoskes wrote:
> > 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.
> >
> > That is an irrelevant comment, because there are prime numbers which
> > are not of that form (like 2).
>
> It is no irrelevant but you have not yet understood my arguing.


No one but WM can understand WM's arguing.


>
> > Er ... Euclid proved that there are an _infinite_ number of primes.
>
> Euclid did not talk of infinity. There are more than any given number,
> he said.
>
> > What do you find wrong with that proof?
>
> Do you really think it necessary to demonstrate such things here?


Does WM really think it necessary to avoid everything that does not
allow him to obsure the real isues?

> Recently we had a proof that sqrt(2) is not rational. We should
> concentrate on more general problems: It is impossible to label more
> than 10^100 entities by all particles the univese supplies. Therefore
> there cannot exist a set with more than 10^100 elements and we cannot
> count up to 10^10^100.


What happens in the physical world does not govern what happens in an
axiom system. Such systems are not subject to any physical limitations
but only the limitations of what the axioms themselves state and the
imaginations of those who investgate them.
>
> Regards, WM
>
> Regards, WM
.