> On Saturday, 16 August 2014 21:49:03 UTC+2, Ben Bacarisse wrote: > > >> | can you show a formula of set theory involving your bijection f form Z >> | to Z (f(x) = x + 1) which is false in set theory and true with the >> | correct "interpretation of infinity"? (Or vice versa of course.) > > It is not easy to find a difference between a bijection that is > claimed an actually infinite set and a potentially infinite bijection > between two equal sets. That's the reason why set theory could exist > for such a long time! The striking argument was always the > countability of |N "by definition" and in the potential sense.
I thought not.
> Therefore I have applied two different sets. If actual infinity is > assumed, then one of the sets gets exhausted before the other. This is > a result of mathematics, but onlz if infinitz is actual. Otherwise we > have the bijection going on and on. But such a set would never supply > an anti-diagonal or a complete list of all algebraics. It is this > subtle switching infinities that has gone unnoticed for such a long > time.