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Topic: ? 533 Proof
Replies: 46   Last Post: Aug 4, 2014 8:39 PM

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Virgil

Posts: 10,821
Registered: 6/8/11
Re: ? 533 Proof
Posted: Aug 3, 2014 6:04 PM
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In article <0039a748-767b-4228-91ff-0a5ef66853ad@googlegroups.com>,
mueckenh@rz.fh-augsburg.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 order-isomorphically
to the standard ordering of |N by means of a general definition of an
order-relations on |Q which well-order |Q order-isomorphically to |N and
thus bijects |N and |Q.

And each of those well-orderings of Q disproves WM's false claim that
no such bijecting well-orderings are possible.

Here is a straightforward way to construct a well-ordering 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 well-ordering 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 well-order 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 well-ordering 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
anti-mathemtaics.
--
Virgil
"Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)




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