Cauchy Schwarz say that $$\mid x_1y_1\mid +...+ \mid x_ny_n\mid \leq \sqrt{x_1^2+...+x_n^2}\sqrt{y_1^2+...+y_n^2}.$$ (This follows from the popular proof using AM-GM.)
This is Holder's inequality with conjugate pairs (2,2) if you like. But it seems like everyone writes it as $$\mid x_1y_1+...+ x_ny_n\mid \leq \sqrt{x_1^2+...+x_n^2}\sqrt{y_1^2+...+y_n^2}.$$ The second one follows from the first one but the first one does not follow from the second, so why is the second way of writing it vastly more popular?