Triangle Inequality/Real Numbers/Proof 2

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

This can be seen to be a special case of Minkowski's Inequality for Sums, with $n = 1$.

$\blacksquare$

Sources

• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 1$: Real Numbers: $\S 1.17$