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Topic: looking for example of closed set that is *not* complete in a metric space
Replies: 26   Last Post: Feb 3, 2013 11:06 AM

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 Shmuel (Seymour J.) Metz Posts: 3,473 Registered: 12/4/04
Re: looking for example of closed set that is *not* complete in a metric space
Posted: Feb 3, 2013 11:06 AM

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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Date Subject Author
2/1/13 Achimota
2/1/13 Paul
2/1/13 Paul
2/1/13 fom
2/1/13 fom
2/2/13 Shmuel (Seymour J.) Metz
2/3/13 fom
2/3/13 Shmuel (Seymour J.) Metz
2/2/13 Achimota
2/2/13 Butch Malahide
2/2/13 quasi
2/2/13 Butch Malahide
2/2/13 Achimota
2/2/13 quasi
2/3/13 Achimota
2/3/13 Paul
2/3/13 Achimota
2/1/13 Butch Malahide
2/1/13 J. Antonio Perez M.
2/1/13 William Hughes
2/2/13 J. Antonio Perez M.
2/1/13 Butch Malahide
2/1/13 William Elliot
2/2/13 Butch Malahide
2/2/13 William Elliot
2/2/13 Butch Malahide
2/2/13 Shmuel (Seymour J.) Metz