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Re: looking for example of closed set that is *not* complete in a metric space
Posted:
Feb 3, 2013 11:06 AM
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In <BNKdnX3mxd460ZPMnZ2dnUVZ_sudnZ2d@giganews.com>, on 02/03/2013
at 05:40 AM, fom <fomJUNK@nyms.net> said:
>That is not me.
It bears your name, and you didn't give a citation to show that the
words were someone else's.
>The construction of the reals from the natural numbers
>is a sequence of logical types for which the order relation of the
>natural numbers grounds the order relation of the derived type.
What is at issue is treating convergent Cauchy sequences as a separate
type rather than a special case.
>You can find an excellent construction of the integers in Jacobson:
Has it changed in the last half century?
>From this, one constructs the reals. The following
>is from Cantor's Grundlagen concerning the logic
>of definition for a real number:
He, or your translation, fails to distinguish between set and
sequence. To which real number does the set {1/2,1/3} correspond?
--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
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