> On Monday, 18 August 2014 05:40:22 UTC+2, Ben Bacarisse wrote: >> email@example.com writes: >> >> > The striking argument was always the >> > countability of |N "by definition" and in the potential sense.
This time the hard bit you snipped was my asking:
| 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.)
and it was your admission that you can not provide such a thing the prompted me to say:
>> I thought not. >> > Most mathematicians don't even know that "finished infinity" is more > than a joke.
Some, like you, appear not to be able to define it without more undefined words. Maybe you can show a formula, involving some infinite set, that is true in set theory with its "finished infinities" and false otherwise (or vise versa of course)? You can't do for bijections between sets, but maybe you can for just a set.
>> > It is this >> > subtle switching infinities that has gone unnoticed for such a long >> > time. >> >> Same mathematics, different words. > > No. But difficult to see the difference, without my proof.
A formula, provably true in one and false in another, would be a start. The only proof I've see is of a formula that is true in set theory. presumably it's true in your world too. So far, all the same mathematics, despite the dramatic words.