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Topic: Joel David Hamkins on definable real numbers in analysis
Replies: 98   Last Post: Jun 30, 2013 3:22 PM

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Joel David Hamkins on definable real numbers in analysis
Posted: Jun 28, 2013 4:34 AM

On Thursday, June 27, 2013 11:54:40 PM UTC-7, muec...@rz.fh-augsburg.de wrote:
> On Thursday, 27 June 2013 20:21:47 UTC+2, Virgil wrote:
>

> > In article <28b6c17f-0950-46de-a125-70baec6a079f@googlegroups.com>, muec...@rz.fh-augsburg.de wrote: > On Wednesday, 26 June 2013 17:48:25 UTC+2, dull...@sprynet.com wrote:
>
>
>

> > > > >For all n exists k: d_1, d_2, d_3, ..., d_n = q_k1, q_k2, q_k3,...,q_kn. >This theorem it is not less important than Cantor's theorem: For all >k: d =/= q_k. Both theorems contradict each other.
>
>
>

> > > > Erm, no they don't. If your "for every n there exists k such that" was > > instead "there exists k such that for every n" then they would contradict > > each other.
>
>
>

> >> Try to find a d_n that, together with all its predecessors d_j for 0 < j < n, is not in a q_k. Then you may boast "erm". Otherwise learn that, in mathematics, there is no continuation of d beyond every d_n.
>
>
>

> > But there is a continuation beyond ANY d_n, which is
>
>
>
> which is realized by digits d_n with larger n. You cannot excape.
>
>
>
> "There exists k such that for every n: a_kn = d_n" is a contradiction for dummies.
>

So, you can prove that a collection of finite decimal sequences
contains an infinite one.

IF: An infinite collection of finite decimal sequences, when written in one line, makes an actually infinite collection,
THEN: an infinite collection of finite decimal sequences written in different lines does the same.
(Unioning over subsets cannot not extend a set.)

>
> "For every n there exists k such that a_kn = d_n" is a contradiction for mathematicians who take the trouble to try to escape it - without success, of course.
>

That doesn't imply, "There exist m e N, such that a_m = d."

That is your uneducated or miseducated guess.
Prove it by finding any digit of d that is not, together will all its predecessors, in an a_m.
You will fail. Therefore your statement is wrong.
(It has been transferred without sufficient reason from non-linear sets like knifes and forks. But in this case forking is invalid, as invalid as forcing in general).
If there is a set of FISONs that contains every natural number n and all its predecessors, then this set cntains |N. nN? Is there something in |N that is outside of all its FISONs?

Regards, WM

Date Subject Author
6/18/13 fom
6/19/13 David Petry
6/19/13 fom
6/19/13 mueckenh@rz.fh-augsburg.de
6/19/13 Peter Percival
6/19/13 mueckenh@rz.fh-augsburg.de
6/19/13 Virgil
6/19/13 Tucsondrew@me.com
6/21/13 David C. Ullrich
6/21/13 mueckenh@rz.fh-augsburg.de
6/21/13 Virgil
6/22/13 mueckenh@rz.fh-augsburg.de
6/22/13 Virgil
6/22/13 mueckenh@rz.fh-augsburg.de
6/22/13 Virgil
6/22/13 mueckenh@rz.fh-augsburg.de
6/22/13 Tucsondrew@me.com
6/22/13 mueckenh@rz.fh-augsburg.de
6/22/13 Tucsondrew@me.com
6/23/13 mueckenh@rz.fh-augsburg.de
6/23/13 Tucsondrew@me.com
6/23/13 Tucsondrew@me.com
6/23/13 mueckenh@rz.fh-augsburg.de
6/23/13 Tucsondrew@me.com
6/23/13 Virgil
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6/24/13 Virgil
6/23/13 Virgil
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6/23/13 Virgil
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6/24/13 mueckenh@rz.fh-augsburg.de
6/24/13 Virgil
6/25/13 Virgil
6/25/13 Virgil
6/26/13 Virgil
6/26/13 fom
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6/22/13 Virgil
6/22/13 Tucsondrew@me.com
6/22/13 mueckenh@rz.fh-augsburg.de
6/22/13 Virgil
6/22/13 David C. Ullrich
6/22/13 mueckenh@rz.fh-augsburg.de
6/22/13 Virgil
6/23/13 David C. Ullrich
6/23/13 mueckenh@rz.fh-augsburg.de
6/23/13 Virgil
6/24/13 mueckenh@rz.fh-augsburg.de
6/24/13 Virgil
6/25/13 mueckenh@rz.fh-augsburg.de
6/25/13 Virgil
6/24/13 David C. Ullrich
6/24/13 mueckenh@rz.fh-augsburg.de
6/24/13 Virgil
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6/25/13 Virgil
6/26/13 mueckenh@rz.fh-augsburg.de
6/26/13 Virgil
6/25/13 Tucsondrew@me.com
6/26/13 mueckenh@rz.fh-augsburg.de
6/26/13 Virgil
6/26/13 mueckenh@rz.fh-augsburg.de
6/26/13 Virgil
6/26/13 David C. Ullrich
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6/26/13 Virgil
6/27/13 mueckenh@rz.fh-augsburg.de
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6/27/13 mueckenh@rz.fh-augsburg.de
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6/28/13 mueckenh@rz.fh-augsburg.de
6/28/13 Tucsondrew@me.com
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6/28/13 Tucsondrew@me.com
6/28/13 mueckenh@rz.fh-augsburg.de
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6/29/13 mueckenh@rz.fh-augsburg.de
6/29/13 Virgil
6/30/13 Virgil
6/28/13 Virgil
6/29/13 mueckenh@rz.fh-augsburg.de
6/29/13 Virgil
6/28/13 Virgil
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6/19/13 Virgil
6/19/13 Virgil