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

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 Tucsondrew@me.com Posts: 1,161 Registered: 5/24/13
Re: Matheology § 285
Posted: Jun 13, 2013 12:24 PM

On Thursday, June 13, 2013 3:01:00 AM UTC-7, muec...@rz.fh-augsburg.de wrote:
> On Wednesday, 12 June 2013 23:51:52 UTC+2, Zeit Geist wrote:
>

> > On Wednesday, June 12, 2013 12:43:37 PM UTC-7, muec...@rz.fh-augsburg.de wrote:
>
> >
>
> > Choose any q e Q.
>
> >
>
> > For you algorithm to work, we have to be able
>
> >
>
> > find a step n_1 where that 1/2 of the rationals
>
> >
>
> > less than q are well-ordered, a step n_2 where
>
> >
>
> > 2/3 of the rations less than q are well-ordered,
>
> >
>
> > and so on for all numbers in form of n/n+1.
>
>
>
> Same requirement could be required and not be satisfied in the process of enumerating the rationals. Never 2/3 of all rationals less than q are enumerated. That's just what I wanted to show.
>

You are so lost.
I didn't say 1/2 then 2/3 then 3/4 then ... of all Q.

I said for each particular q e Q, you must be able to
produce a natural number m_(1/2) such that at step
m(1/2) we have for at least one-half of all rationals p,
p < q, p is in the natural order.

Indeed for any real, r, you must be able to find a
natural number m_(r); where if E(q) is the natural
number index of q in the enumeration, then at
step m_(r) you have ceiling( r * E(q) ) of the rationals
less than q in their proper position in the enumeration.
Actually, you just need to show they are in a position
less than E(q) at step m_(r). Since the property must be
true for all q e Q, the fact that must be eventually be in
proper order eventually does follow.

>
> > This will never happen in you algorithm,
>
> >
>
> > so you never well-order all rationals in their
>
> >
>
> > order of magnitude.
>
>
>
> And this will never happen in countaing the rationals. Thanks.
>

For a general well-ordering of the rationals, not in order of magnitude,
we don't have to worry about, say, 1/2 of the rations less than q.
We just have to worry about, say, 1/2 the rationals, p, such that E(p) < E(q).

It is the "in order of magnitude" part that make it a different situation.

>
> 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.