Put in Interval Notation Calculator
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Interval notation is a concise way to represent sets of real numbers. This calculator helps you convert between different representations of intervals, including inequalities, number lines, and interval notation syntax.
What is Interval Notation?
Interval notation is a mathematical shorthand used to describe ranges of real numbers. It's commonly used in calculus, algebra, and other branches of mathematics to represent intervals on the real number line.
Interval notation uses parentheses ( ) and square brackets [ ] to indicate whether endpoints are included or excluded in the interval.
Key Symbols in Interval Notation
- [a, b] - Includes all numbers from a to b, including a and b
- (a, b) - Includes all numbers from a to b, excluding a and b
- [a, b) - Includes all numbers from a to b, including a but excluding b
- (a, b] - Includes all numbers from a to b, excluding a but including b
- (a, ∞) - All numbers greater than a
- (-∞, b) - All numbers less than b
- (-∞, ∞) - All real numbers
When to Use Interval Notation
Interval notation is particularly useful when:
- Describing the domain of a function
- Specifying solution sets to equations
- Working with inequalities
- Analyzing limits and continuity
How to Use This Calculator
Our interval notation calculator makes it easy to convert between different representations of intervals. Here's how to use it:
- Select the type of interval you want to convert from in the dropdown menu
- Enter the appropriate values in the input fields
- Click "Calculate" to see the interval notation result
- Review the explanation and example provided
The calculator supports conversion from inequalities, number line descriptions, and other interval formats to standard interval notation.
Interval Notation Formulas
Here are the key formulas used in interval notation:
Closed Interval: [a, b] = {x | a ≤ x ≤ b}
Open Interval: (a, b) = {x | a < x < b}
Half-Open Intervals: [a, b) = {x | a ≤ x < b} and (a, b] = {x | a < x ≤ b}
Infinite Intervals: (a, ∞) = {x | x > a} and (-∞, b) = {x | x < b}
These formulas provide the mathematical foundation for interval notation and help explain how different interval types are represented.
Common Interval Notation Examples
Here are some common examples of interval notation and their interpretations:
| Interval Notation | Description | Number Line Representation |
|---|---|---|
| [2, 5] | All real numbers from 2 to 5, including 2 and 5 | •••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••••• |