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

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 285
Posted: Jun 12, 2013 5:51 PM

On Wednesday, June 12, 2013 12:39:58 PM UTC-7, muec...@rz.fh-augsburg.de
wrote:

>
> > > Every configuration can be well-ordered by size.
> This implies there is no q that stays outside the well order.

Let's see WM well-order the integers by size, including all the
negative ones. Or even only the negative ones.

Until he can show us a well-ordering by size of such a simple ordered
but not well-ordered set, we can ignore his wild claims.

>
>

> > Every finite one can, but not the entire set of Q.
>
>
>
> I prove that all elements of Q can be well-ordered by size.

You only claim it but you do not prove it.
> You cannot disprove it, because you cannot find any element
> that stays outside, can you?

But we can find nested sequences of well-ordered sets whose union/limit
set is not well-ordered.
Let S_n = { -k : k in FISON(k)}
Then each S_N is finite and well-ordered
(note that every finite ordered set is automatically well-ordered)

But the union of all S_n. the sequence of S_n's defined above.'s, being
the set of negative integers, is not well-ordered. Thus there must be
something wrong with WM's "proof".

What is wrong is that WM assumes that a nested sequences of well-ordered
sets must have a well ordered limit/union set, which is obviously not
the cse, at lest not outside his wild weird world of WMytheology.

WM's Conjecture: a nested increasing sequence of well-ordered sets must
have a well-ordered limit/union set.

Disproof: the S_n = { -k : k in FISON(k)} define above.

>
> > Any finite set of real numbers can be well- according to magnitude. ones, not necessarily.
>
Not necessarily when outside the wild weird world of WMytheology.
Counterexample above.
>
> Either find a q that stays outside of the well-order by size. If such a q exists and is enumerated as q_n, then there is a first natural number n that cannot be put in a permutation such that all q's are in order by size. If such a q exists and cannot be enumerated, then countability is nonsense.
>
>
>
> I claim: Every set of natural numbers can be put in every desired permutation. Among them there is the permutation that orders Q by size.
>

Sure thing.
If the enumeration has f(j) = 1/2,
what is f(j+1), f(j+2) and f(j+3)?

If f keeps the order we must have

| f(m) | <= | f(m+1) |

And no rational r, such that the magnitude
Of r is in between that of f(m) and f(m+1).

>
> Regards, WM

ZG
--

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.