Interval Notation Online Tutoring - Maths Tutors

Interval Notation Online Tutoring - Maths Tutors 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