# Intervals

An **interval** is a to set of real numbers between two given points: **a and b**, which are called** ends of the interval**.

#### Open Interval

**An open interval**,** (a, b)**, is the set** of all real numbers greater than a and smaller than b.**

**(a, b) = {x / a < x < b} **

#### Closed Interval

**A closed interval**,** [a, b]**, is the set** of all real numbers greater than or equal to a and less than or equal to b**.

**[a, b] = {x / a ≤ x ≤ b}**

#### Half-Closed Intervals

**(a, b] = {x / a < x ≤ b}**

**[a, b) = {x / a ≤ x < b}**

Half-closed intervals are also called half-open intervals.

When there are a set of points formed by two or more of these intervals, the sign (**Union**) is used between them.

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