Re: Finite : A definition

On Mar 19, 4:46 pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:

However, I don't think you need it for your definition. All you need
is that any infinite ordinal is 1-1 with some other ordinal. If I'm
not mistaken, we can prove that in Z.

It occurred to me that my proof used 'w'. But a nice feature of the
Tarski-based definitions is that we can state them easily and easily
prove certain equivalences without having to first define 'w'. Of
course, even though I used 'w', I could have eliminated the symbol in
my argument by using elimination of defined symbols, but then that
would detract from the aura of simplicity it seems you're working for.
Now, if you have a much different proof, simple, and not involving
'w', then that's fine too.

MoeBlee
.