How to Write and Understand Interval Notation in Maths
Interval Notation Calculator
What is Interval Notation Calculator?
An Interval Notation Calculator is an easy-to-use tool that helps you convert mathematical statements involving inequalities or solution sets into interval notation. Interval notation is a concise way to represent sets of numbers that lie between specific endpoints, stating clearly whether those endpoints are included or not. With this calculator, you can enter inequalities like x > 3, double inequalities such as 2 ≤ x < 7, or expressions like x ≠ 0, and instantly get the answer in standardized interval notation format.
Formula or Logic Behind Interval Notation Calculator
The calculator works by recognizing common forms of mathematical inequalities and mapping them to interval notation using these key rules:
- '(' or ')' symbols indicate the endpoint is not included (an open interval).
- '[' or ']' symbols indicate the endpoint is included (a closed interval).
- The symbol '∞' (infinity) or '−∞' is used for unbounded intervals and is always paired with round brackets, since infinity is not a number you can reach.
- Compound statements (like 'x ≤ 0 or x > 5') are represented as a union (∪) of two intervals.
Inequality to Interval Notation Conversion Table
| Inequality | Interval Notation |
|---|---|
| a < x < b | (a, b) |
| a ≤ x ≤ b | [a, b] |
| a < x ≤ b | (a, b] |
| a ≤ x < b | [a, b) |
| x > a | (a, ∞) |
| x ≥ a | [a, ∞) |
| x < b | (−∞, b) |
| x ≤ b | (−∞, b] |
| x ≠ c | (−∞, c) ∪ (c, ∞) |
| all real numbers | (−∞, ∞) |
Steps to Use the Interval Notation Calculator
- Enter your inequality, range, or solution set in the input box (e.g., x ≥ 0 and x < 5, or x ≠ 2).
- Click on the 'Calculate' button.
- Get instant results: View the interval notation along with step-by-step explanation.
Why Use Vedantu’s Interval Notation Calculator?
Vedantu’s Interval Notation Calculator is quick, accurate, and designed for mobile and desktop. It’s trusted by students across India and beyond for exam revision, homework, and clarity on set and interval notation. The intuitive interface makes entering math expressions stress-free, and the detailed steps help you learn while you calculate. You can also explore related math tools such as the HCF Calculator and Prime Numbers lookup as you prepare for exams or solve assignments.
Real-life Applications of Interval Notation Calculator
Understanding interval notation is useful in many scenarios such as:
- Describing temperature ranges (e.g., safe storage ranges for food or medicine).
- Reporting exam cutoffs (“marks between 35 and 100 inclusive” as [35, 100]).
- Engineering tolerances (acceptable measurements for parts, e.g., [1.2, 1.5] mm).
- Filtering data sets in computer programs or statistics.
- Stating age or eligibility brackets, for offers or rules (e.g., [18, 60) years).
If you're studying algebra or set theory, try using Vedantu’s Algebra Topics or get more practice with Factors and Multiples in Maths. These resources, along with the Interval Notation Calculator, can boost your clarity and confidence in mathematics.
