I want to test some \$$\LaTeX \$$ out.

**Definition.** A **monotone function** from a preorder \$$(X,\le_X)\$$ to \$$(Y,\le_Y)\$$ is a function \$$f : X \to Y\$$ such that the following diagram commutes,

$$\large\begin{matrix} x & \overset{\le_X}{\longrightarrow} & x' \\\\ f\downarrow & & \downarrow f \\\\ f(x) & \overset{\le_Y}{\longrightarrow} & f(x') \end{matrix}$$

for all elements \$$x,x' \in X\$$.