PrepZii

table

Finite Interval Types

The handbook defines intervals as subsets of $\mathbb{R}$ used in inequalities and domains.

Interval	Set form	Endpoint note
Open	$(a,b)=\{x:a<x<b\}$	Endpoints not included
Closed	$[a,b]=\{x:a\le x\le b\}$	Endpoints included; source notes this is possible only when both $a$ and $b$ are finite
Open-closed	$(a,b]=\{x:a<x\le b\}$	Left endpoint open, right endpoint closed
Closed-open	$[a,b)=\{x:a\le x<b\}$	Left endpoint closed, right endpoint open

$a$

constant, endpoint, or first term

$b$

constant or endpoint

$x$

variable