1.5 Intervals

Intervals are segments of the real line. We define:

$(a,b)=\{x\in{\mathbb{R}}:a<x<b\},$ the open interval from $a$ to $b$, excluding the endpoints;

$[a,b]=\{x\in{\mathbb{R}}:a\leq x\leq b\},$ the closed interval from $a$ to $b$ including the endpoints;

$(-\infty,\infty)={\mathbb{R}}$; the symbol $\infty$ stands for infinity, which is not a real number;

$[0,\infty)=\{x\in{\mathbb{R}}:x\geq 0\}$, the set of non-negative real numbers.