On 18/06/2010 10:40 AM, Transfer Principle wrote: > On Jun 17, 6:56 am, Sylvia Else<syl...@not.here.invalid> wrote: >> On 15/06/2010 2:13 PM, |-|ercules wrote: >>> the list of computable reals contain every digit of ALL possible >>> infinite sequences (3) >> Obviously not - the diagonal argument shows that it doesn't. > > But Herc doesn't accept the diagonal argument. Just because > Else accepts the diagonal argument, it doesn't mean that > Herc is required to accept it. > > Sure, Cantor's Theorem is a theorem of ZFC. But Herc said > nothing about working in ZFC. To Herc, ZFC is a "religion" > in which he doesn't believe.
Well, if he's not working in ZFC, then he cannot make statements about ZFC, and he should state the axioms of his system.
> > Else's post, therefore, is typical of the posts which seek > to use ZFC to prove Herc wrong.
Part of the problem, as others have noted, lies in determining what it is that Herc thinks he's proving. His assertions become inpenetrable as an increasing function of their distance from the start of his posting.