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Topic: Every Subspace of R^N has an Orthogonal Basis?
Replies: 175   Last Post: Jul 4, 2006 9:20 AM

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 Mariano Posts: 1,900 Registered: 8/22/05
Re: Every Subspace of R^N has an Orthogonal Basis?
Posted: Jun 28, 2006 12:36 PM

Lee Rudolph wrote:
> Virgil <vmhjr2@comcast.net> writes:
>

> >Besides which, one can make
> >almost any set into a vector space with enough warping.

>
> Of course that depends on one's (necessarily [?] informal) notion of
> what "almost any" might mean when applied to the universe of sets,
> but among the finite sets, "one can make" such a set X "into a
> vector space" if and only if X has cardinality p^n for some prime
> p and non-negative integer n; and I think it's fair (if not formally
> justified) to say that not "almost any set" of finite cardinality
> is a set of cardinality a prime power. No doubt some of the local
> aficionados of non-naive set theory can inform us accurately of which
> familiar set theoretical axioms allow one to conclude that few, many, or
> "almost" all infinite sets are in bijection with some vectorspace.

"Almost any set" in this context means: "any set with either infinite
cardinality or a finite prime power cardinality", as those are the
cardinals of vector spaces.

-- m

Date Subject Author
6/26/06 Hatto von Aquitanien
6/26/06 Lee Rudolph
6/26/06 Jose Carlos Santos
6/26/06 Hatto von Aquitanien
6/26/06 Jose Carlos Santos
6/26/06 Hatto von Aquitanien
6/26/06 magidin@math.berkeley.edu
6/26/06 Robert Low
6/26/06 James Dolan
6/26/06 Hatto von Aquitanien
6/26/06 magidin@math.berkeley.edu
6/26/06 Hatto von Aquitanien
6/26/06 magidin@math.berkeley.edu
6/26/06 Hatto von Aquitanien
6/26/06 magidin@math.berkeley.edu
6/27/06 Hatto von Aquitanien
6/27/06 Virgil
6/27/06 Hatto von Aquitanien
6/27/06 Gene Ward Smith
6/27/06 Hatto von Aquitanien
6/28/06 Brian Quincy Hutchings
6/27/06 Michael L. Siemon
6/27/06 Hatto von Aquitanien
6/27/06 Michael L. Siemon
6/27/06 Virgil
6/27/06 magidin@math.berkeley.edu
6/27/06 Tim Golden http://bandtech.com
6/27/06 magidin@math.berkeley.edu
6/28/06 David C. Ullrich
6/28/06 Tim Golden http://bandtech.com
6/28/06 magidin@math.berkeley.edu
6/28/06 Tim Golden http://bandtech.com
6/29/06 Robert Low
6/29/06 Tim Golden http://bandtech.com
6/29/06 David C. Ullrich
6/27/06 Dave Seaman
6/27/06 Hatto von Aquitanien
6/27/06 David C. Ullrich
6/27/06 Hatto von Aquitanien
6/27/06 David C. Ullrich
6/27/06 magidin@math.berkeley.edu
6/26/06 Virgil
6/29/06 Pinky
6/29/06 Hatto von Aquitanien
6/26/06 Gene Ward Smith
6/27/06 Hatto von Aquitanien
6/27/06 Virgil
6/27/06 Hatto von Aquitanien
6/27/06 Gene Ward Smith
6/27/06 Hatto von Aquitanien
6/27/06 Gene Ward Smith
6/27/06 Gene Ward Smith
6/27/06 Hatto von Aquitanien
6/27/06 Gene Ward Smith
6/27/06 Mariano
6/26/06 Virgil
6/27/06 Hatto von Aquitanien
6/27/06 Virgil
6/27/06 Hatto von Aquitanien
6/27/06 Virgil
6/28/06 Hatto von Aquitanien
6/28/06 David C. Ullrich
6/28/06 Hatto von Aquitanien
6/29/06 David C. Ullrich
6/29/06 Hatto von Aquitanien
6/29/06 David C. Ullrich
6/29/06 Lee Rudolph
6/29/06 K. E. Pledger
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6/29/06 Denis Feldmann
6/29/06 Hatto von Aquitanien
6/29/06 Denis Feldmann
6/29/06 Hatto von Aquitanien
6/29/06 Virgil
6/29/06 magidin@math.berkeley.edu
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6/29/06 Gene Ward Smith
6/29/06 Hatto von Aquitanien
6/29/06 magidin@math.berkeley.edu
6/29/06 Hatto von Aquitanien
6/28/06 magidin@math.berkeley.edu
6/27/06 David C. Ullrich
6/26/06 Jose Carlos Santos
6/26/06 David C. Ullrich
6/26/06 Robert Low
6/26/06 David C. Ullrich
6/26/06 David C. Ullrich
6/26/06 Hatto von Aquitanien
6/26/06 Robert Low
6/26/06 magidin@math.berkeley.edu
6/26/06 Hatto von Aquitanien
6/26/06 David C. Ullrich
6/27/06 kunzmilan@atlas.cz
6/27/06 Hatto von Aquitanien
6/27/06 Robert Low
6/27/06 Lee Rudolph
6/27/06 Denis Feldmann
6/27/06 Hatto von Aquitanien
6/27/06 Robert Low
6/28/06 David C. Ullrich
6/28/06 Hatto von Aquitanien
6/29/06 David C. Ullrich
6/29/06 Hatto von Aquitanien
6/29/06 Virgil
6/30/06 Hatto von Aquitanien
6/30/06 Denis Feldmann
6/30/06 Hatto von Aquitanien
6/30/06 Denis Feldmann
6/27/06 Hatto von Aquitanien
6/28/06 Robert Low
6/27/06 Denis Feldmann
6/27/06 David C. Ullrich
6/27/06 Virgil
6/28/06 Hatto von Aquitanien
6/28/06 Robert Low
6/28/06 Hatto von Aquitanien
6/28/06 Robert Low
6/28/06 Gene Ward Smith
6/28/06 Hatto von Aquitanien
6/28/06 Hatto von Aquitanien
6/28/06 Lee Rudolph
6/28/06 Mariano
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6/29/06 Lee Rudolph
6/29/06 magidin@math.berkeley.edu
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6/29/06 Lee Rudolph
6/30/06 Bertie Reed
6/30/06 Denis Feldmann
6/30/06 Mariano
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6/30/06 Mariano
6/30/06 Aatu Koskensilta
7/2/06 Shmuel (Seymour J.) Metz
7/2/06 Herman Rubin
7/2/06 Denis Feldmann
6/29/06 Mariano
6/29/06 Gene Ward Smith
6/28/06 David C. Ullrich
6/29/06 Hatto von Aquitanien
6/29/06 Virgil
6/29/06 Robert Low
6/29/06 Lee Rudolph
6/29/06 Virgil
6/29/06 Lee Rudolph
6/29/06 Virgil
6/29/06 W. Dale Hall
6/30/06 Robert Low
6/30/06 Virgil
6/30/06 Hatto von Aquitanien
6/30/06 Virgil
6/30/06 Hatto von Aquitanien
6/30/06 magidin@math.berkeley.edu
7/1/06 Hatto von Aquitanien
7/1/06 magidin@math.berkeley.edu
7/2/06 Hatto von Aquitanien
7/2/06 Denis Feldmann
7/2/06 David C. Ullrich
7/2/06 Hatto von Aquitanien
7/2/06 magidin@math.berkeley.edu
7/3/06 Gerry Myerson
7/3/06 Hatto von Aquitanien
7/3/06 David C. Ullrich
7/3/06 magidin@math.berkeley.edu
7/3/06 Hatto von Aquitanien
7/3/06 magidin@math.berkeley.edu
7/3/06 Hatto von Aquitanien
7/3/06 Virgil
7/3/06 David C. Ullrich
6/30/06 Robert Low
6/29/06 Hatto von Aquitanien
6/29/06 Virgil
6/29/06 Hatto von Aquitanien
6/29/06 Virgil
7/4/06 kunzmilan@atlas.cz
7/4/06 Lee Rudolph