Interval.notation Calculator

Interval notation is a way to represent a set of real numbers using parentheses and brackets. This calculator helps you convert between interval notation and inequality notation.

What is Interval Notation?

Interval notation is a concise way to represent a range of real numbers. It uses parentheses and brackets to indicate whether the endpoints are included or excluded from the interval.

There are four types of intervals:

(a, b) - Open interval: a and b are not included
[a, b] - Closed interval: a and b are included
(a, b] - Half-open interval: a is not included, b is included
[a, b) - Half-open interval: a is included, b is not included

Interval notation is commonly used in calculus, algebra, and other branches of mathematics to describe domains, ranges, and solution sets.

How to Use the Calculator

Our interval notation calculator makes it easy to convert between interval notation and inequality notation. Simply enter your interval in one format, and the calculator will display the equivalent in the other format.

Step-by-Step Guide

Select whether you want to convert from interval notation to inequality notation or vice versa.
Enter your interval in the selected format.
Click the "Calculate" button to see the result.
Review the result and use it in your mathematical work.

Formula:

For interval notation to inequality: Replace parentheses with inequalities and brackets with equal signs.
For inequality to interval notation: Replace inequalities with parentheses and equal signs with brackets.

Examples

Here are some examples of how to use the interval notation calculator:

Example 1: Interval Notation to Inequality

Convert the interval [2, 5) to inequality notation.

Solution: The interval [2, 5) represents all real numbers x such that 2 ≤ x < 5.

Example 2: Inequality to Interval Notation

Convert the inequality -3 < x ≤ 10 to interval notation.

Solution: The inequality -3 < x ≤ 10 represents the interval (-3, 10].

Interval Notation	Inequality Notation
(a, b)	a < x < b
[a, b]	a ≤ x ≤ b
(a, b]	a < x ≤ b
[a, b)	a ≤ x < b

FAQ

What is the difference between parentheses and brackets in interval notation?

Parentheses ( ) indicate that the endpoint is not included in the interval, while brackets [ ] indicate that the endpoint is included. For example, [2, 5) includes 2 but not 5, while (2, 5] includes 5 but not 2.

How do I represent an open interval?

An open interval is represented with parentheses on both ends, such as (a, b), which means all numbers greater than a and less than b.

What is the difference between interval notation and set notation?

Interval notation is a shorthand way to represent a set of real numbers, while set notation uses curly braces and lists the elements. For example, the interval [1, 5] is equivalent to the set {1, 2, 3, 4, 5} in set notation.