# Interval Notation

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Interval notation is a way to express a set of number in the form of an inequality. Usually set of real numbers are represented using the interval notation. There are following types of interval notations:

Open Interval : This is represented are (c, d)

Closed interval: This is represented as [c, d]

Half – Open Interval: This is represented as [c, d) or (c, d]

Non – ending interval: This can be represented as (-∞, c) or (c, ∞).

Example 1: Interpret the following interval notations:

(a)  ( 2, 5 )
(b)   [ 2, 5 )
(c)  ( - 2, 5 ]

Solution: The given interval notations can be interpreted as follows:
(a)  (2,5) : This set consists of all real numbers between 2 and  5 but excluding 2 and 5.
(b)   [ 2, 5 ) : In this set all real numbers between 2 and 5 are included. This set includes 2 but excludes 5.
(c)  ( - 2, 5 ]: In this set all real numbers between -2 and  5 are included. This set excludes -2 but includes 5.

Example 2: Interpret the interval notations given below in the form of inequality:

(a)  ( - ∞, 7)
(b)  (7, ∞)
(c)  [ -6, 7 ]

Solution: Let p be any general element of the given set. Then the given interval notations can be written in the form of an inequality as below:

(a)   ( - ∞, 7) :          p < 7
(b)   (7, ∞):               p > 7
(c)   [ -6, 7 ] :          - 6 ≤ p ≤ 7