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Re: Matheology § 285
Posted:
Jun 11, 2013 3:07 PM
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On Tuesday, June 11, 2013 11:49:59 AM UTC-7, muec...@rz.fh-augsburg.de wrote:
> On Tuesday, 11 June 2013 20:23:17 UTC+2, Julio Di Egidio wrote:
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> >> After each one has been > attached to a natural, we have the set of naturals that obviously can > be re-ordered in any desired way.
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> > Obviously and crucially not in any finite number of steps (you will get the rationals well-ordered by magnitude from, say, the rationals lexicographically ordered). Anyway, I'm already out of my depths here, so I'll leave this to more competent mathematicians.
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> It is obvious: If we show in set theory a proposition P(n) for the first n elements of a well-ordered set (where n is an arbitrarily large natural number), then we do show it for all elements of the set.
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> If we enumerate the rationals, we do it up to n (since there is no infinite natural number). If we apply the diagonal argument, we do it up to n (since there is no infinite natural number). If we well-order the rational numbers by magnitude, we do it up to n.
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> There is absolutely no difference.
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> > (The power set of |N should even include the singleton of the last natural > as an element.) There is no such thing as the last natural number, and not even a next to last, and not even a next to next to last, and so on.
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> I know. But there are more than any natural number of numbers. So if we take the numbers 1 to n for any natural number, then we have less than aleph_0 naturals. What remains to take all?
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> This is but *one* simple aspect which shows that the jerks of matheology should really be imprisonde in a mad-house.
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> It's a bit of a pain to have to reformat your posts and quotes every time: it would help a lot if you could at least split your paragraphs in short lines using carriage returns.
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> That's due to the new Google which is an outspoken shit. Unfortunately it seems that I cannot return to the old version. The developer of that mess be cursed.
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> Regards, WM
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