Let $(X,d_X)$, $(Y,d_Y)$, and $(Z,d_Z)$ be metric spaces. Let $L,M\ge 0$ be [real numbers](/page/Real%20Numbers), let $f:X\to Y$ be an $L$-Lipschitz map, and let $g:Y\to Z$ be an $M$-Lipschitz map. Then the composition $g\circ f:X\to Z$ is $ML$-Lipschitz; that is, for every $x_1,x_2\in X$,