How this calculator works
Parentheses exclude a finite boundary and square brackets include it. One-sided inequalities become rays. A between condition uses both bounds in one interval, while an outside condition joins two rays with U. Infinity is unbounded rather than an attainable endpoint, so it always uses a parenthesis.
Formula
x >= a becomes [a, inf). a < x <= b becomes (a, b]. x < a or x > b becomes (-inf, a) U (b, inf).
Worked example
x >= 3 becomes [3, inf). The condition -1 <= x < 4 becomes [-1, 4). The outside condition x <= -1 or x > 4 becomes (-inf, -1] U (4, inf).
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Frequently asked questions
What if the two bounds are equal?
A between range contains the single point only if both ends include it. Otherwise it is empty.
Does U mean and?
No. It means union: a value can belong to either part. A bounded between interval represents both boundary conditions together.
Can I paste an inequality?
Use the structured controls. This tool does not parse free-form algebraic text.