Calculator
Enter one form, then convert it into interval notation, inequality form, set builder notation, and a graph-ready description.
Example Data Table
| Input Type | Input | Converted Interval | Inequality Form |
|---|---|---|---|
| Interval | [2, 5) | [2, 5) | 2 ≤ x < 5 |
| Inequality | x > 7 | (7, ∞) | x > 7 |
| Set Builder | {x ∈ R : -3 < x ≤ 1} | (-3, 1] | -3 < x ≤ 1 |
| Union | x < -2 or x ≥ 4 | (-∞, -2) ∪ [4, ∞) | x < -2 or x ≥ 4 |
Formula Used
This calculator uses logical boundary rules rather than arithmetic-only evaluation. It checks inclusion, exclusion, infinity direction, and union structure before formatting the equivalent notation.
How to Use This Calculator
- Select the format you are entering.
- Type the interval, inequality, or set builder expression.
- Use the sample dropdown if you want a quick test.
- Press Convert Notation to generate all matching forms.
- Review the converted interval, inequality, set builder, and graph description.
- Download the result as CSV or PDF if needed.
FAQs
1. What does interval notation represent?
Interval notation shows all numbers inside a range. Brackets include endpoints, parentheses exclude endpoints, and unions combine separated solution sets into one expression.
2. Why are infinity symbols always paired with parentheses?
Infinity is not a reachable endpoint. Because it cannot be included as an actual number, interval notation always uses parentheses beside positive or negative infinity.
3. How is a closed endpoint different from an open endpoint?
A closed endpoint means the boundary value belongs to the solution set. An open endpoint means the solution approaches that value but does not include it.
4. Can the calculator convert compound inequalities?
Yes. It can read chained inequalities such as 2 ≤ x < 7 and convert them into interval, set builder, and graph description outputs.
5. Does it support unions of intervals?
Yes. You can enter unions using U or the word “or,” depending on the selected input style, and the calculator will preserve separated regions.
6. What is set builder notation in this tool?
Set builder notation describes a set using a variable and a condition, such as {x ∈ R : x > 3}. The calculator converts that condition into interval form.
7. Can this calculator draw the graph automatically?
It gives a graph-ready description instead of plotting directly. That description explains shading direction and whether each endpoint is open or closed.
8. When should I use a union symbol?
Use a union when the solution has separate ranges. For example, x < -1 or x ≥ 4 becomes two intervals connected by ∪.