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PROOF OF CAUCHY–SCHWARZ INEQUALITY
/latexit \begin{align*}|x+y|&\leq|x|+|y|\\{|x+y|}^2&\leq{|x|}^2+{|y|}^2+2|x||y|\\{|x|}^2+{|y|}^2+2xy&\leq{|x|}^2+{|y|}^2+2|x||y|\\2xy&\leq2|x||y|\\xy&\leq|x||y|\\xy&\leq\boxed{|xy|\leq|x||y|}\end{align*
GAUSS'S FLUX THEOREM
/latexit \[ \oint_S E_n dA = \frac{1}{\varepsilon_0} Q_{inside} \]