Let $V$ be an inner product space over $F$. Then for all $x,y \in V$ and $c \in F$,
$\|x+y\|$ $\leq$$\|x\| + \|y\|$. (Triangle Inequality)
The following is a proof of the triangle inequality:
I wanted to know how one gets that $2\Re\langle x,y \rangle \leq 2|\langle x,y\rangle|$, where $\Re $ denotes the real part of the complex number $\langle x,y \rangle$.