Interval Notation Calculator
Convert between interval notation and inequalities with step-by-step explanations
Interval Notation Converter
Common Examples
Inequality to Interval
Interval to Inequality
Notation Guide
Brackets
Inequality Symbols
Special Cases
Quick Tips
Always use parentheses ( ) with infinity symbols
Square brackets [ ] include the endpoint
Parentheses ( ) exclude the endpoint
The left value must be less than the right value
(-∞,∞) represents all real numbers
Understanding Interval Notation
What is Interval Notation?
Interval notation is a mathematical way to describe sets of real numbers between two endpoints. It provides a concise method to represent ranges of values, which is particularly useful in algebra, calculus, and other mathematical contexts.
Types of Intervals
Closed Interval [a,b]
Includes both endpoints: a ≤ x ≤ b
Open Interval (a,b)
Excludes both endpoints: a < x < b
Half-Open Intervals
[a,b) or (a,b]: One endpoint included, one excluded
How to Read Interval Notation
Step-by-Step Guide
- Identify the left bracket: [ (inclusive) or ( (exclusive)
- Read the first number (left endpoint)
- Note the comma separator
- Read the second number (right endpoint)
- Identify the right bracket: ] (inclusive) or ) (exclusive)
Example: [2,7)
This represents all real numbers from 2 to 7, including 2 but excluding 7. In inequality form: 2 ≤ x < 7
Special Cases
Unbounded Intervals
- (-∞,a]: x ≤ a
- (a,∞): x > a
- [a,∞): x ≥ a
All Real Numbers
(-∞,∞) represents the entire real line
Empty Set
∅ or represents no solutions