Search All of the Math Forum:

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

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

Topic: Matheology § 285
Replies: 84   Last Post: Jun 15, 2013 6:05 PM

 Messages: [ Previous | Next ]
 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 285
Posted: Jun 12, 2013 2:32 PM

mueckenh@rz.fh-augsburg.de wrote:

> On Wednesday, 12 June 2013 00:03:13 UTC+2, Virgil wrote:
>

> > to enumerate the rationals, that ennumeration goes on not only up to but
> > also past every n.

>
> You claim that induction shows that the rationals can be enumerated? No
> problem. See below.
>

> > First you must show us your claimed well-ordering by magnitude of the
> > negative integer rationals.

>
> So if you want to enumerate *all* rationals, you first must enumerate the
> integers. You are great! Really!

If you claim to have an enumeration of all rationals, you must have, in
passing, an ennumeation of every subset of the rationals as well.

And if there is some subset which WM says cannot be ennumerated, how
does WM plan to claim ennumeration any of its supersets?
>
> > If you cannot even do that then you will fail with any superset of all
> > rationals.

>
> Induction shows that the rationals can be well-ordered by size.

It only shows that any finite subset of rationals can be well-ordered by
size, but every FINITE ordered-set is automatically well-ordered, and a
only infinite sets can be not well-ordered.

So until WM can produce an explicit example of an infinite set which is
both densely ordered and well-ordered, he is merly faking things again,
as usual.

For every
> well-orderable-by-size
> configuration n: {q_1, q_2, ..., q_n}
> there is the well-orderable-by-size
> configuration n+1: {q_1, q_2, ..., q_n+1}.
> And there is no rational q_n in the complete list of all rationals that lacks
> a natural number n or lacks a place in the well-orderable-by-size
> configurations from n to every desired number.
>
> Regards, WM

--

Date Subject Author
6/11/13 mueckenh@rz.fh-augsburg.de
6/11/13 Virgil
6/11/13 JT
6/11/13 Tucsondrew@me.com
6/11/13 mueckenh@rz.fh-augsburg.de
6/11/13 Virgil
6/11/13 Tucsondrew@me.com
6/11/13 mueckenh@rz.fh-augsburg.de
6/11/13 Tucsondrew@me.com
6/11/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Tucsondrew@me.com
6/12/13 Virgil
6/11/13 Tucsondrew@me.com
6/11/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Tucsondrew@me.com
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/12/13 Tucsondrew@me.com
6/13/13 mueckenh@rz.fh-augsburg.de
6/13/13 Tucsondrew@me.com
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Tucsondrew@me.com
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Tucsondrew@me.com
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Tucsondrew@me.com
6/15/13 Virgil
6/15/13 Tanu R.
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/15/13 Virgil
6/14/13 Virgil
6/13/13 Virgil
6/12/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/12/13 Tucsondrew@me.com
6/12/13 Virgil
6/13/13 mueckenh@rz.fh-augsburg.de
6/13/13 Virgil
6/11/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Tucsondrew@me.com
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/12/13 Scott Berg
6/12/13 Virgil
6/12/13 Tucsondrew@me.com
6/13/13 mueckenh@rz.fh-augsburg.de
6/13/13 Virgil
6/12/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/11/13 LudovicoVan
6/11/13 mueckenh@rz.fh-augsburg.de
6/11/13 LudovicoVan
6/11/13 mueckenh@rz.fh-augsburg.de
6/11/13 Tucsondrew@me.com
6/11/13 Tucsondrew@me.com
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Tucsondrew@me.com
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/12/13 Tucsondrew@me.com
6/12/13 Virgil
6/12/13 Virgil
6/13/13 mueckenh@rz.fh-augsburg.de
6/13/13 Virgil
6/12/13 Virgil
6/11/13 LudovicoVan
6/11/13 Virgil
6/11/13 Tanu R.
6/11/13 Tucsondrew@me.com
6/11/13 Tucsondrew@me.com
6/11/13 Tucsondrew@me.com
6/11/13 Virgil
6/11/13 Tanu R.
6/11/13 Virgil
6/11/13 Tanu R.