# Definition:Real Interval/Unit Interval/Open

## Definition

The open interval between $0$ and $1$ is referred to as the open unit interval.

$\left({0 \,.\,.\, 1}\right) = \left\{ {x \in \R: 0 < x < 1}\right\}$

## Notation

An arbitrary interval is frequently denoted $\mathbb I$, although some sources use just $I$. Others use $\mathbf I$.

### Wirth Interval Notation

The notation used on this site to denote a real interval is a fairly recent innovation, and was introduced by Niklaus Emil Wirth:

 $\displaystyle \openint a b$ $:=$ $\displaystyle \set {x \in \R: a < x < b}$ Open Real Interval $\displaystyle \hointr a b$ $:=$ $\displaystyle \set {x \in \R: a \le x < b}$ Half-Open (to the right) Real Interval $\displaystyle \hointl a b$ $:=$ $\displaystyle \set {x \in \R: a < x \le b}$ Half-Open (to the left) Real Interval $\displaystyle \closedint a b$ $:=$ $\displaystyle \set {x \in \R: a \le x \le b}$ Closed Real Interval

The term Wirth interval notation has consequently been coined by $\mathsf{Pr} \infty \mathsf{fWiki}$.