Virgil
Posts:
10,821
Registered:
6/8/11


Re: ? 533 Proof
Posted:
Aug 3, 2014 6:04 PM


In article <0039a748767b422891ff0a5ef66853ad@googlegroups.com>, mueckenh@rz.fhaugsburg.de wrote:
> On Sunday, 3 August 2014 16:38:53 UTC+2, V I R G I L wrote: > > > > > > What N does that no finite initial segment of N does is contain ALL > > finite initial segments of N as proper subsets, so N does things that > > no finite initial segment of N can do. > > And for just all these finite initial segments I have shown that they leave > infinitely many, in fact increasingly many, rationals without index. Whereas > you show your enumerations only for some 10 naturals. Feeble. WM lies! Actually what I HAVE shown is at least two slightly different bijections between N and Q, each by ordering Q orderisomorphically to the standard ordering of N by means of a general definition of an orderrelations on Q which wellorder Q orderisomorphically to N and thus bijects N and Q.
And each of those wellorderings of Q disproves WM's false claim that no such bijecting wellorderings are possible.
Here is a straightforward way to construct a wellordering of the positive rationals. Write each one as p/q where naturals p and q have no common factor (other than 1). Order them by ascending value of (p+q), then within each set of p+q values, order by ascending p.
So everyone but WM gets t the wellordering of Q+ starting with: 1/1, 1/2, 2/1, 1/3, 3/1, 1/4, 2/3, 3/2, 4/1, ...
Anyone other than WM can then wellorder the whole set of rationals, Q, by putting zero first then interleaving each negative after its corresponding positive in the above ordering.
So everyone but WM understands the wellordering of Q starting with: 0/1, 1/1, 1/1, 1/2, 1/2, 2/1,2/1, 1/3, 1/3, 3/1, 3.1, 1/4, 1/4, 2/3, 2/3, 3/2, 3/2, 4/1,4/1, ...
And everyone but WM now understands that WM is hereby proved totally and irrevocably wrong! And that WM's worthless world of WMytheology is antimathemtaics.  Virgil "Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)

