Date: Feb 3, 2013 11:06 AM
Author: Shmuel (Seymour J.) Metz
Subject: Re: looking for example of closed set that is *not* complete in a metric space

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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