Math snippets

Compare $R^+$ with $A = \left\{ x^2 | x \in R^+ \text{ and } x \ne 0 \right\}$, note that $m \in R^+$ iff $m \in A$.

Cauchy–Schwarz inequality in vector form:
$\left| a \cdot b \right| \le \left| a \right| \left| b \right|$

We have two seqs: $a_n = 1/n, b_n = 1/n^2$, where $n = 2, 3, 4, 5, ...$. Obviously $a_n > b_n$, but
$$\lim_{ n \rightarrow \infty } a_n = \lim_{ n \rightarrow \infty } b_n$$

Proposition: generalize the triangle inequality to multi-angle inequality: