Recent content by joecharland

I have worked my way though the proof of the Cauchy Schwarz inequality in Rudin but I am struggling to understand how one could have arrived at that proof in the first place. The essence of the proof is that this sum: ##\sum |B a_j - C b_j|^2## is shown to be equivalent to the following...

Can anyone tell me if the below proof is correct? Also how can I format my TEX differently so that it all works properly on this site? Lemma - if $A$ and $B$ are sets of positive real numbers, put $ AB = \left\{ ab | a \in A, b \in B \right\}$. Then $\sup AB = \sup A \sup B$. \\ Clearly...