Solve Interval Notation Brackets Calculator

Interval notation is a concise way to represent sets of real numbers. This calculator helps you convert between bracket notation and interval notation, which is essential for understanding mathematical ranges and inequalities.

What is Interval Notation?

Interval notation is a method of representing a set of real numbers that lie between two endpoints. It's commonly used in mathematics, particularly in calculus and algebra, to describe ranges of values.

There are two main types of brackets used in interval notation:

Square brackets [ ] - Indicates that the endpoint is included in the interval
Parentheses ( ) - Indicates that the endpoint is not included in the interval

For example, the interval [2, 5] includes all real numbers from 2 to 5, including 2 and 5 themselves. The interval (2, 5) includes all real numbers between 2 and 5, but not 2 or 5.

Types of Brackets in Interval Notation

Understanding the difference between the two types of brackets is crucial for accurate interval representation:

Bracket Type	Symbol	Meaning	Example
Closed (inclusive)	[ ]	Endpoint is included	[3, 7] includes 3 and 7
Open (exclusive)	( )	Endpoint is not included	(3, 7) excludes 3 and 7
Half-open	[ ) or ( ]	One endpoint included, one excluded	[3, 7) includes 3 but excludes 7

Example

The interval (0, 100) represents all real numbers greater than 0 and less than 100, while [0, 100] includes both 0 and 100.

Converting Between Notations

Converting between bracket notation and interval notation is a straightforward process. Here's how to do it:

Identify the lower and upper bounds of the interval
Determine whether each bound is included or excluded
Use the appropriate brackets to represent the interval

Conversion Formula

If you have an inequality like a ≤ x ≤ b, it converts to the interval [a, b]. If it's a < x < b, it converts to (a, b).

Common Interval Examples

Here are some common interval notations and their meanings:

Interval Notation	Description	Example Values
(-∞, ∞)	All real numbers	...-3, -2, -1, 0, 1, 2, 3...
[0, ∞)	All non-negative real numbers	0, 1, 2, 3, 4, ...
(-∞, 0]	All non-positive real numbers	...-3, -2, -1, 0
(a, b)	All numbers between a and b, not including a and b	If a=2, b=5: 2.1, 2.5, 4.9
[a, b]	All numbers between a and b, including a and b	If a=2, b=5: 2, 2.5, 5

Frequently Asked Questions

What does the interval [3, 7) mean?

The interval [3, 7) includes all real numbers greater than or equal to 3 and less than 7. It includes 3 but excludes 7.

How do I convert an inequality to interval notation?

For an inequality like 2 ≤ x < 5, you would write the interval as [2, 5). The first number uses a square bracket because it's included, and the second number uses a parenthesis because it's excluded.

What does the interval (-∞, 0) represent?

The interval (-∞, 0) represents all real numbers less than 0. It includes negative numbers but excludes 0.