Definition:Real Interval/Notation/Conventional

Definition

These are the notations usually seen for real intervals:

$\ds \left ({a, b}\right)$

$:=$

$\ds \set {x \in \R: a < x < b}$

$\ds \left [{a, b}\right)$

$:=$

$\ds \set {x \in \R: a \le x < b}$

$\ds \left ({a, b}\right]$

$:=$

$\ds \set {x \in \R: a < x \le b}$

$\ds \left [{a, b}\right]$

$:=$

$\ds \set {x \in \R: a \le x \le b}$

but they can be confused with other usages for this notation.

In particular, there exists the danger of taking $\paren {a, b}$ to mean an ordered pair.