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

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Posts: 10,821
Registered: 6/8/11
Re: ? 533 Proof
Posted: Aug 3, 2014 6:04 PM
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In article <>, 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:
1/2, 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:
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
"Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)

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