# Triangle Inequality/Real Numbers/Proof 3

## Theorem

Let $x, y \in \R$ be real numbers.

Let $\size x$ denote the absolute value of $x$.

Then:

$\size {x + y} \le \size x + \size y$

## Proof

We have that Real Numbers form Ordered Integral Domain.

Therefore Sum of Absolute Values on Ordered Integral Domain applies directly.

$\blacksquare$