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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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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Joel David Hamkins on definable real numbers in analysis
Posted: Jun 26, 2013 5:53 PM

In article <u43ms8do4814dgi1l1b0fh79ju5r42teu3@4ax.com>,
dullrich@sprynet.com wrote:

> On Tue, 25 Jun 2013 13:43:36 -0700 (PDT), mueckenh@rz.fh-augsburg.de
> wrote:
>

> >On Tuesday, 25 June 2013 17:07:36 UTC+2, dull...@sprynet.com wrote:
> >>> There are not uncountably many reals, neither in the natural order nor in
> >>> the well-order.

> >
> >

> >> That's very funny.
> >
> >That's easily provable:
> >
> >Consider a Cantor-list that contains a complete sequence (q_k) of all
> >rational numbers q_k. The first n digits of the anti-diagonal d are
> >d_1, d_2, d_3, ..., d_n. It can be shown *for every n* that the Cantor-
> >list beyond line n contains infinitely many rational numbers q_k that
> >have the same sequence of first n digits as the anti-diagonal d.
> >
> >Proof: There are infinitely many rationals q_k with this property. All
> >are in the list by definition. At most n of them are in the first n
> >lines of the list. Infinitely many must exist in the remaining part of
> >the list. So we have obtained:
> >
> >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
>
> that way is very common among people who haven't learned
> to reason carefully.
>
>

> >with the result that finished
> >infinity as presumed for transfinite set theory is not a valid
> >mathematical notion.
> >
> >Regards, WM

WM's quantifier dyslexia strikes again!

WM will never be able to make it as a mathematician until he cures his
quantifier dyslexia.

And also escape from the other corruptions of his wild weird world of
WMytheology
--

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
6/23/13 Virgil
6/24/13 Virgil
6/23/13 Virgil
6/22/13 Virgil
6/23/13 mueckenh@rz.fh-augsburg.de
6/23/13 Virgil
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 Virgil
6/25/13 Virgil
6/26/13 Virgil
6/26/13 fom
6/26/13 Virgil
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
6/25/13 David C. Ullrich
6/25/13 mueckenh@rz.fh-augsburg.de
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
6/26/13 mueckenh@rz.fh-augsburg.de
6/26/13 Virgil
6/27/13 mueckenh@rz.fh-augsburg.de
6/27/13 Virgil
6/26/13 Virgil
6/27/13 mueckenh@rz.fh-augsburg.de
6/27/13 Virgil
6/28/13 mueckenh@rz.fh-augsburg.de
6/28/13 Tucsondrew@me.com
6/28/13 mueckenh@rz.fh-augsburg.de
6/28/13 Tucsondrew@me.com
6/28/13 mueckenh@rz.fh-augsburg.de
6/28/13 Tucsondrew@me.com
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
6/28/13 Virgil
6/19/13 Virgil
6/19/13 Virgil