# Interval Notation

## Interval Notation

Interval notation is a method of representing a set of real numbers by combining symbols and numbers. It is normally used in mathematics to represent the set of all real numbers that a function or variable can accept.

## The three main types of intervals are:

Open intervals: An open interval is a set of real numbers that consists of all the numbers between two given values, but excludes the values themselves. It is marked using parentheses, such as this: (a, b). As an example, the open interval (2, 5) denotes all numbers between 2 and 5, excluding the 2 and 5 themselves.

Closed intervals: A closed interval is a set of real numbers that consists of all the numbers between two given values, and also the values themselves. It is marked by square brackets, like this: [a, b]. As an example, the closed interval [2, 5] denotes all real numbers between 2 and 5, and also the 2 and 5 themselves.

Half-open intervals: A half-open interval is a set of real numbers that consists of all the real numbers between two given values, but only retains one of the values itself. It is marked by both parentheses and square brackets, like this: (a, b] or [a, b). As an example, the half-open interval (2, 5] represents all real numbers between 2 and 5, and also 5, but leaves 2.

In interval notation, the use of the symbols "-infinity" and "infinity", is also possible to depict negative and positive infinity, respectively. As an example, the interval (-infinity, 5) denotes all numbers that are less than 5, and the interval [2, infinity) denotes all numbers greater than or equal to 2.

Interval notation is a straightforward and very efficient way to represent sets of real numbers, and it is frequently used in mathematics and other fields to represent data or value ranges.