On Wednesday, 6 August 2014 17:15:26 UTC+2, Zeit Geist wrote: > On Wednesday, August 6, 2014 6:49:59 AM UTC-7, muec...@rz.fh-augsburg.de wrote: > > > > > Up to every desired n and q_n. Alas they belong to a finite initial segment. Infinitely many follow. The infinite is never completed. > > > > You try to Show a Contradiction in Set Theory
I have shown a contradiction between set theory and mathematics.
> so you take True Statements and Mix them with False Statements. In Set Theory, there does Not Exist any Infinite Sets that are Not "Complete". There simply ARE Infinite Sets. We Understand that you do Not like this Concept, but it is No way in Contradiction with the Other Axioms. You are free to Use a System with No Infinite Sets.
You are free to maintain set theory, although it has not the least application to anything but set theory. But, pleeeeze, don't confuse it with mathematics. Set theorists cannot be convinced by me, classical mathematicians cannot be convinced by you. More cannot be said. It is as it is. > > > > > No complete bijection such that no element is missing, no complete list (with respect to the natural numbers) so that another element, the "anti-diagonal", could not be enumerated. >
> Are we talking Rationals or Reals here? Anti-diagonal?
Uncountability is a consequence of completeness of countable sets. Many set theorists don't like to know that in set theory infinity sets have to be complete. But otherwise Cantor's diagonal arguments fails.