Cauchy Schwarz Proof
This is one of my favorite math proofs! Usually the Cauchy-Schwarz inequality is proven using projections, but this proof is completely elementary. It is taken from Pugh's Real Mathematical Analysis-book. But beware it doesn't work for complex inner product spaces. Bon appétit! :) Note: I forgot to mention: If a = 0, then v = 0, but then the statement is trivial.
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