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Re: Matheology § 200
Posted:
Jan 26, 2013 5:44 PM
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On Saturday, January 26, 2013 10:24:04 AM UTC+2, WM wrote:
> Matheology § 200
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>
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> We know that the real numbers of set theory are very different from
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> the real numbers of analysis, at least most of them, because we cannot
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> use them. But it seems, that also the natural numbers of analysis 1,
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> 2, 3, ... are different from the cardinal numbers 1, 2, 3, ...
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>
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> This is a result of the story of Tristram Shandy, mentioned briefly in
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> § 077 already, who, according to Fraenkel and Levy ["Abstract Set
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> Theory" (1976), p. 30] "writes his autobiography so pedantically that
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> the description of each day takes him a year. If he is mortal he can
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> never terminate; but if he lived forever then no part of his biography
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> would remain unwritten, for to each day of his life a year devoted to
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> that day's description would correspond."
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>
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> This result is counter-intuitive, but set theory needs the feature of
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> completeness for the enumeration of all rational numbers. If not all
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> could be enumerated, the same cardinality of |Q and |N could not be
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> proved.
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>
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> However recently a formal contradiction with the corresponding limit
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> of real analysis could be shown:
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> http://planetmath.org/?op=getobj&from=objects&id=12607
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> and here
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> http://www.hs-augsburg.de/medium/download/oeffentlichkeitsarbeit/publikationen/forschungsbericht_2012.pdf
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> on p. 242 - 244
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> The limit of remaining unwritten days is infinite according to
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> analysis whereas Fraenkel's story is approved by set theory.
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>
>
> Nevertheless, matheologians deny every contradiction. One of them,
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> Michael Greinecker (as a self-proclaimed watchdog, and bouncer in
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> MathOverflow
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> http://meta.mathoverflow.net/discussion/1296/crank-post-to-flag-as-spam/#Item_0
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> an interbreeding of Tomás de Torquemada and Lawrenti Beria) stated:
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> "there is no contradiction. Just a somewhat surprising result.
Poor WM: his last intent to have some of his trash published in SE received a rather quick "close thread" and, as with any otherclsoed threads, it vanished into oblivion.
Oh, well: perhaps next time.
Tonio
"It's tough to be a crank in SE, dudes!"
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