Re: Two results of set geometry

Tony Orlow wrote:
If each is the last plus 1, then the nth is n, and there cannot be n of
them without n being in the set. That's basic logic. No non-logical (ala
Ross) axioms required. It's pre-axiomatic, and therefore has precedence.


David R Tribble wrote:
I see at least three axioms being used there. Do you?
Hint: What does "n plus 1" mean?


Tony Orlow wrote:
Hint: It doesn't matter, if the size and max of the set start out equal,
and have "+1" simultaneously applied. x+1=x+1 by simple identity.

"Identity" being a kind of axiom, no doubt, like the Identity axiom
of PA.

Do it y times, and x+y=x+y. I don't need any axioms to note that the same
string is on both sides of the equal sign.

How do you define the '=' and the '+' operators without axioms?

.

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