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How many proofs of the Cauchy-Schwarz inequality are there? Is there some kind of reference that lists all of these proofs?

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    I've slightly edited the body your question in order to make it self-contained. I've also added the `real-analysis` tag.2011-02-24
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    I would try the book "The Cauchy-Schwarz Masterclass".2011-02-24
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    @user3533: excellent. I got that book. It seems that this textbooks also talks about few other inequalities that I was going to study. Do you know any other references that basically is about different kind of inequalities and their proofs? Thanks2011-02-24
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    @Vafa: many Olympiad preparation books include sections on inequalities. There is also Kedlaya's notes: http://www.artofproblemsolving.com/Resources/Papers/KedlayaInequalities.pdf2011-02-24
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    Found Inequalities By Hardy, too: http://www.amazon.com/Inequalities-Cambridge-Mathematical-Library-Hardy/dp/05213588092011-02-24
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    Your first question is essentially unanswerable, except, maybe, by "many"...2011-02-24
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    @Vafa Khalighi: It is Hardy, Littlewood (Author) and Pólya.2011-03-01
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    @Vafa Khalighi: Here is a link that gives 12 different proofs of the Cauchy-Schwarz that may be of interest to you. http://ajmaa.org/RGMIA/papers/v12e/Cauchy-Schwarzinequality.pdf2012-07-02

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