In article <email@example.com>, firstname.lastname@example.org wrote:
> On Monday, 15 July 2013 18:23:40 UTC+2, Zeit Geist wrote: > > > > > > > > > Any finite set of Naturals is a subset of infinitely many line, > > The infinite set of naturals is nothing else than all finite sets of > naturals.
Wrong!, It is notmerely a set of sets of naturals, as you wold have it, but the union of such a set of sets, that is to say it is also a set of naturals.
> What else should define it (in mathematics with finite naturals - > not in matheology with infinite beliefs).
Given any set of sets, in a set theory such as ZF, there is a inion set whose members are exactly the members of members of the original set of sets.
Thus in any decent set theory, if every natural is in a set of naturals, say its FISON, then the union of all FISONs exists and is the set of all naturals. So that outside of WM's wild weird world of WMytheology, there is a set of naturals, and inside WM's wild weird world of WMytheology there no coherent way of dealing with the notion of sets at all. > > > > but no infinite set of Naturals is a subset of any line. > > Let the sets where they belong, namely in matheology. Let's talk math, namely > about numbers.
Set theory is as much part of modern mathematics in the 21st century as any other area of mathematics, and those who reject it are not 21st century mathematicians, or even 20th century mathematicians, and are bad even as 19th century mathematicians. --