# Definition:Real Interval/Half-Open

Jump to: navigation, search

## Definition

Let $a, b \in \R$.

There are two half-open (real) intervals from $a$ to $b$.

#### Right half-open

The right half-open (real) interval from $a$ to $b$ is the subset:

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

#### Left half-open

The left half-open (real) interval from $a$ to $b$ is the subset:

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

## Also known as

This can often be seen rendered as half open interval.

## Examples

### Example $1$

Let $I$ be the unbounded closed real interval defined as:

$I := \hointr 1 2$

Then $1 \in I$.