Triangle Inequality/Examples/4 Points

Theorem
Let $M = \struct {A, d}$ be a metric space.

Let $x, y, z, t \in A$.

Then:
 * $\map d {x, z} + \map d {y, t} \ge \size {\map d {x, y} - \map d {z, t} }$

Proof
We have that $\map d {x, z}$, $\map d {y, t}$, $\map d {x, y}$, $\map d {z, t}$ are themselves all real numbers.

Hence the Euclidean metric on the real number line can be applied: