Triangle Inequality/Real Numbers/Proof 3
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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.
$\blacksquare$