In article <email@example.com>, firstname.lastname@example.org 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?
> > > > 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. If there are countably many members to a set it stays counable. 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.
> > > You might be able to construct an add function, but, from my experience, > > simple properties like associativity and commutativity seem to be > > impossible to establish. Addition, multiplication and exponentiation must > > be closed on the natural numbers. > > Of course. That is the problem pointing to neither finite nor actually > infinite mathematics.
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.
< Potential infinity appears to be the only resolution
Only in WM's wild weird world of WMytheology. Elsewhere, at least in mathematics, one either has actual finiteness or actual infiniteness. --