# The open interval and the closed interval ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1, Problem 3RCC
To determine

## To find:The open interval and the closed interval

Expert Solution

Open interval (a,b)

={xR|a<x<b} and closed interval [a,b]

={xR|axb}

### Explanation of Solution

Given:

Open interval (a,b) and closed interval [a,b]

Concept used:

(a,b)=]a,b[={xR|a<x<b}

[a,b]={xR|axb}

Calculation:

A interval is a set of real numbers that contains all real numbers lying between any two numbers of the set

An open interval does not include its endpoints

An open interval is denoted as (a,b)

For example :- (0,1) means greater than 0 and less than 1

Open interval form is

(a,b)=]a,b[={xR|a<x<b}

A closed interval is an interval which includes all limit points

Closed interval is denoted as [a,b]

For example :- [0,1]

Closed interval form is

[a,b]={xR|axb}

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