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Re: Finitely definable reals.
Posted:
Jan 14, 2013 8:23 AM
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On Saturday, January 12, 2013 12:24:46 AM UTC-8, WM wrote:
> On 12 Jan., 02:14, Virgil <vir...@ligriv.com> wrote:
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> > > Cantor managed to prove that there are more than countably many finite
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> > > binary strings possible. Remember, the part behind a_nn of a_n is not
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> > > relevant for his proof.
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> > Quite so, but that in no way weakens his proof.
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> It shows a self-contradiction by the fact that there must be an
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> antidiagonal that from every entry differs at a finite place. But if
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> the list is complete with respect to all finite binary strings, this
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> is obviously impossible.
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> Regards, WM
I've been thinking about this assertion of your and beg to differ.
The decimal expansion of 1/3 only differs from all other reals at
the infinite. It takes the infinite to make it 1/3. When one multiplies
a number by 10 one moves the decimal place one position to the right.
Only the infinite decimal expansion will do to restore the fraction.
Any finite expansion will have a delta from 1/3.
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