Re: Relative Cardinality

In article <ITSnetNOTcom#virgil-3668F6.21373406072005@xxxxxxxxxxxxxxxxxxxxxxxx>,
Virgil <ITSnetNOTcom#virgil@xxxxxxxxxxx> wrote:
>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?

Isn't this basically the position of the ultrafinitists? I'm not sure
how seriously they are taken in the field and I'm not sure if WM's
position is as well thought out as theirs, but is it fundamentally
irrational or unmathematical?

OTOH, we should could have saved a lot of time debating this if he'd just
said up front what his objection was.

Alan
--
Defendit numerus
.

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