On Friday, 2 May 2014 18:13:46 UTC+2, Virgil wrote: > In article <firstname.lastname@example.org>, > > email@example.com wrote: > > > > > On Thursday, 1 May 2014 22:41:27 UTC+2, Dan Christensen wrote: > > > > On Tuesday, April 29, 2014 2:50:51 AM UTC-4, muec...@rz.fh-augsburg.de > > > > wrote: > > > > > > > > > Couldn't just the seemingly so fruitful hypothesis of the infinite have > > > > > straightly inserted contradictions into mathematics and have > > > > > fundamentally distroyed the basic nature of this science which is so > > > > > proud on its consistency? > > > > It didn't! > It is easy to prove that it did because Zermelo did not understand what infinity is. It is infinite, i.e., without end. > > > > > > > > Whoever said it has obviously not tried to formalize number theory on a > > > finite set of any size (one with a beginning and an end). > > > > > > Set theory shows the uncountability of all countably many finite > > expressions. > > > > Not outside of WM's wild weird world of WMytheology, it doesn't.
Can you quote any "uncountability proof" that constructs an undefinable number? Or that implies the existence of undefinable numbers? Or that ends without a real number that has been defined by this proof?
> > If there are countably many members to a set it stays counable.
Of course. > > It is the set of all subsets of a coutnably infinite set that becomes > uncountable, which is quite different from what WM s flasely claims > above. > Hessenberg's "proof" constructs one and only one subset. Of course this subset is amply defined. I think it has been defined more than 100000 times. Therefore we have 100000 space-time quadruples and 100000 names of authors or readers and in addition the general definition of this set: The set of all natural numbers that are not mapped on sets containing them. Few item in mathematics have been better definid. >
> But in a set of naturals which is not actually infinite one one cannot > have n+1 > n for all n in such a set.
One can. Otherwise classical mathematics would be self-contradictory, and we had to use MatheRealism.