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Spivak Calculus 3rd ed. $|a + b| \leq |a| + |b|$
I'm working through the first chapter of Michael Spivak's Calculus 3rd ed.
Towards the end of the chapter he proves $ |a + b| ≤ |a| + |b| $ using the observation that $|a|= \sqrt{ a^2 }$ when $a$ ...
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Two Analysis Questions
1) Define : $\langle z\rangle := (1+|z|^2 ) ^\frac{1}{2} $ for all $z \in \mathbb{C} $.
Prove : $\langle x+y\rangle \leq 2\langle x\rangle\langle y\rangle $ for all $x,y \in \mathbb{R} ^N$ .
2) ...
