In article <firstname.lastname@example.org>, email@example.com wrote:
> 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.
WM may have shown a contradiction between set theory and WM's worthless world of WMytheology , but that worthless world of WMytheology is quite different from any proper mathematics, whether finitist or infinitist. > > > > 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.
How does WM do topology without any sets or set theory? Or does WM claim that topology is not a part of modern mathematics?
How does WM do analysis without the set theory required to deal with domains, codomains and ranges of functions. How does WM do geometry without sets of points to represent various geometric figures?
Can WM even name any area of modern mathematics entirely free of any use of sets or set theory? I doubt it!
> Set theorists cannot be convinced by me, classical > mathematicians cannot be convinced by you. More cannot be said. It is > as it is.
Until WM can name a few areas of MODERN mathematics that nowdays still rejects any and all references to sets, he remains a loser.
> > 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.
The standard usage of "set" requires that every statement of the form "x a member of set y" be either true or false, tertium non datur.
In WM's worthless world of WMytheology, not only does tertium datur, but also quarto et quintus et cetera. -- Virgil "Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)