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: $\S 1.17$
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