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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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David C. Ullrich

Posts: 21,553
Registered: 12/6/04
Re: Every Subspace of R^N has an Orthogonal Basis?
Posted: Jul 3, 2006 8:13 AM
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On Mon, 03 Jul 2006 04:36:51 -0400, Hatto von Aquitanien
<abbot@AugiaDives.hre> wrote:

>Arturo Magidin wrote:
>

>> There is a simple reason for that: you don't understand either what
>> you quote or what you see. You have misunderstood that quote pretty
>> much the same way that you have misunderstood the definition of
>> "subspace", of "linear combination", and of pretty much everything you
>> have quoted from any topic in mathematics.
>>
>> You have misinterpreted what "abstraction" means; you seem to think it
>> means "to ignore that which may be imprecise".
>>
>> Mathematics requires abstraction; but it also requires precision. You
>> lack the latter, and you wouldn't know the former if it stripped
>> naked, painted itself purple, and stood on top of a piano with a big
>> "Hello! I'm abstraction" while yelling at the top of its lungs.

>
>Can you explain what Currying is? How exactly does it relate to arity?


What in the world could your point be?

Yes, currying has something to do with abstraction. No, knowing
what currying is does not imply that you understand abstraction
in mathematics. No, the fact that you know what currying is does
not imply that any of the nonsense you've posted these last few
weeks is correct.

Currying is a concept in computer science. If f(x,y) is a binary
function then the curried function f(x) is an unary function
such that f(x)(y) = f(x,y). So what?

************************

David C. Ullrich


Date Subject Author
6/26/06
Read Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Lee Rudolph
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Jose Carlos Santos
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Jose Carlos Santos
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
James Dolan
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gene Ward Smith
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Brian Quincy Hutchings
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Michael L. Siemon
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Michael L. Siemon
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Tim Golden http://bandtech.com
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Tim Golden http://bandtech.com
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Tim Golden http://bandtech.com
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Tim Golden http://bandtech.com
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Dave Seaman
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Pinky
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gene Ward Smith
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gene Ward Smith
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gene Ward Smith
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gene Ward Smith
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gene Ward Smith
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Mariano
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/29/06
Read "dimensionality" v. "dimension" (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Lee Rudolph
6/29/06
Read Re: "dimensionality" v. "dimension" (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
K. E. Pledger
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Denis Feldmann
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Denis Feldmann
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gene Ward Smith
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Jose Carlos Santos
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/26/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
kunzmilan@atlas.cz
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Lee Rudolph
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Denis Feldmann
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Denis Feldmann
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Denis Feldmann
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Denis Feldmann
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/27/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gene Ward Smith
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Lee Rudolph
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Mariano
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Mariano
6/29/06
Read Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Lee Rudolph
6/29/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
magidin@math.berkeley.edu
6/29/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Shmuel (Seymour J.) Metz
6/29/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Lee Rudolph
6/30/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Bertie Reed
6/30/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal
Basis?)
Denis Feldmann
6/30/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Mariano
6/30/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal
Basis?)
Denis Feldmann
6/30/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Mariano
6/30/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal
Basis?)
Aatu Koskensilta
7/2/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Shmuel (Seymour J.) Metz
7/2/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Herman Rubin
7/2/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal
Basis?)
Denis Feldmann
6/29/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Mariano
6/29/06
Read Re: Cardinals of fields (was, Re: Every Subspace of R^N has an Orthogonal Basis?)
Gene Ward Smith
6/28/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Lee Rudolph
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Lee Rudolph
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
W. Dale Hall
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
7/1/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
7/1/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
7/2/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
7/2/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Denis Feldmann
7/2/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
7/2/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
7/2/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Gerry Myerson
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
magidin@math.berkeley.edu
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
7/3/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
David C. Ullrich
6/30/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Robert Low
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Hatto von Aquitanien
6/29/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Virgil
7/4/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
kunzmilan@atlas.cz
7/4/06
Read Re: Every Subspace of R^N has an Orthogonal Basis?
Lee Rudolph

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