Difference between revisions of "Talk:Cauchy-Schwarz Inequality"
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USAMO 1995 number 5 is a great problem solving example.--[[User:MCrawford|MCrawford]] 15:22, 18 June 2006 (EDT) | USAMO 1995 number 5 is a great problem solving example.--[[User:MCrawford|MCrawford]] 15:22, 18 June 2006 (EDT) | ||
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| + | == "not really a proof" == | ||
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| + | Any two vectors define a plane; in that plane, we can measure the angle between them, and CS is then equivalent to the fact that the cosine of this angle is less than 1 in absolute value. This is just as much a proof of CS (taking for granted some simple facts about the geometry of <math>{\bf R}^n</math>) as it is the reverse -- if you think these facts about <math>{\bf R}^n</math> are "less basic" than CS, feel free to add a proof of CS using "more basic" things. --[[User:JBL|JBL]] 15:58, 9 April 2008 (UTC) | ||
Revision as of 10:58, 9 April 2008
USAMO 1995 number 5 is a great problem solving example.--MCrawford 15:22, 18 June 2006 (EDT)
"not really a proof"
Any two vectors define a plane; in that plane, we can measure the angle between them, and CS is then equivalent to the fact that the cosine of this angle is less than 1 in absolute value. This is just as much a proof of CS (taking for granted some simple facts about the geometry of 
) as it is the reverse -- if you think these facts about are "less basic" than CS, feel free to add a proof of CS using "more basic" things. --JBL 15:58, 9 April 2008 (UTC)
