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Interval Notation Converter — result sheet
Build an interval and its matching inequality from finite or unbounded endpoints, endpoint inclusion, and an open or closed boundary choice.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: A finite interval uses a square bracket when its endpoint is included and a parenthesis when it is excluded; infinity always uses a parenthesis. The inequality uses the matching < or ≤ boundary.
The converter keeps the two common descriptions of a real-number set together: interval notation is compact, while the inequality makes endpoint inclusion explicit. It also handles one-sided and all-real intervals without pretending infinity is an ordinary endpoint.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Lower endpoint — minimum -1000000000000; maximum 1000000000000
- Upper endpoint — minimum -1000000000000; maximum 1000000000000
- Lower boundary — 2 choices
- Upper boundary — 2 choices
- Include lower endpoint — 2 choices
- Include upper endpoint — 2 choices
Worked example
| Input | Value |
|---|---|
| Lower endpoint | -2 |
| Upper endpoint | 5 |
| Lower boundary | finite |
| Upper boundary | finite |
| Include lower endpoint | open |
| Include upper endpoint | closed |
Interval = (-2, 5]; inequality = -2 < x ≤ 5; width = 7; midpoint = 1.5.
Assumptions and limits
- Finite endpoints are real numbers and the lower endpoint must be smaller than the upper endpoint when both are finite.
- A square bracket means the finite boundary belongs to the set; a parenthesis means it does not.
- Negative and positive infinity are directions, not values that can be included.
- Only one continuous interval is represented; unions such as (-∞, 1) ∪ (3, ∞) need separate entries.
- The interval describes a mathematical set and does not perform inequality rearrangement from an original expression.
- Decimal endpoints are displayed using the entered numeric values without silently changing precision.
- Use the result as a notation check, then preserve the original inequality conditions in formal work.
- The interval width and midpoint are returned only when both endpoints are finite.
- Endpoint semantics are mathematical conventions and are not a measurement uncertainty statement.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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