The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: § 534 Finis
Replies: 30   Last Post: Feb 22, 2015 8:14 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Virgil

Posts: 10,821
Registered: 6/8/11
Re: � 534 Finis
Posted: Aug 7, 2014 11:57 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article <9c6be357-f362-49d1-9813-67e2c33aec77@googlegroups.com>,
mueckenh@rz.fh-augsburg.de wrote:

> On Thursday, 7 August 2014 00:14:25 UTC+2, Zeit Geist 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.
> >
> > No! You just Think you do.

>
> I think the following: For all natural numbers I have shown that uncounted
> rationals remain.


No, only for each natural number
And since in WM's world "all" is different from "each", he is now
disproved!

And equally many uncounted naturals ALSO remain after each natural.

At least when Q is well-ordered Once again, since WM is having so much
trouble understanding it:

Each member of Q has UNIQUE representation as m/n, with m being an
integer, n being a positive integer, and with m and n having no common
factor greater than 1.

Order them by increasing values of abs(m)+n, and within equal values of
abs(m)+n by increasing values of m, if any.

Note that for positive m, m/1 has successor -(m+1)/1.
For any other form, m/n will have successor of form
(m + k)/(n - k) for some natural k with 0 < k < n.

This is a well-ordering of Q with a first rational, 0/1, and for each
rational a uniquely defined successor rational, and with no rationals
left out.

Thus each rational is now enumerated by the natural number marking its
position in the above well-ordering, at least everywhere outside of
WM's worthless world of WMytheology.
--
Virgil
"Mit der Dummheit kampfen Gotter selbst vergebens." (Schiller)



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.