Re: infinity ...

Albrecht Storz wrote:
>> So, if there is an infinite set there is an infinite number.
>

David R Tribble wrote:
>> Do you mean that an infinite set (or natural numbers) must contain an
>> infinite number as a member (which is false)? Or do you mean that
>> the size of an infinite set is represented by an infinite number
>> (which is partially true)?
>

Albrecht Storz wrote:
> Depending on the axiomatic construction and depending on the necessary
> of truth (since truth means logic consequence) either there are
> infinite natural numbers or there is no infinite set.

Well, then by all means, show us the proof for this, because we don't
believe it. If you're using any non-standard (non-Peano) axioms,
please list those, too.

I've got a set S = {0, 2^0, 2^2^0, 2^2^2^0, ...}, which contains
all the powers of 2 of the form 2^p, where p=0 or 2^q.
1) If it is not an infinite set, tell me how many members it has.
2) If it is an infinite set, tell me what the smallest (first)
infinite number is a member of it.

.

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