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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

On Mon, 03 Jul 2006 04:36:51 -0400, Hatto von Aquitanien

>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 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
6/29/06 Hatto von Aquitanien
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
6/29/06 David C. Ullrich
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
6/28/06 Mariano
6/29/06 Lee Rudolph
6/29/06 magidin@math.berkeley.edu
6/29/06 Shmuel (Seymour J.) Metz
6/29/06 Lee Rudolph
6/30/06 Bertie Reed
6/30/06 Denis Feldmann
6/30/06 Mariano
6/30/06 Denis Feldmann
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