Proof that $d(x,y) = |\frac{1}{x}-\frac{1}{y}|$ defines a Metric
Show that $\left| \frac{1}{x}-\frac{1}{z} \right| \le \left|\frac{1}{x} - \frac{1}{y} \right| + \left|\frac{1}{y} - \frac{1}{z} \right|$.