In this post, I prove that $ |xy| = |x||y|$ in which $x$ is a variable for any real number and $y$ is a variable for any real number. This is done by approximately following the steps in reference [1]. Then I provide a lot of commentary because that is what I like to do. Proof: Note that $x$ can be zero or nonzero, and $y$ can be zero or nonzero–this leads to four cases. The cases involving zero are investigated first. If $x=0$, then $|xy| = |0| = 0 = |0||y| = |x||y|$. If $y=0$, then $|xy| = […]