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Parse interval notation and convert to inequalities, set-builder notation, and graphs
Use ∞ for infinity. Examples: (-∞, 5), [3, 7], (2, ∞), (-∞, 2) ∪ (5, ∞)
Interval notation is a concise way to represent continuous ranges of real numbers. It uses brackets and parentheses to indicate whether endpoints are included or excluded.
Type "infinity", "inf", or "∞". The calculator accepts all formats and will parse them correctly.
(3, 7) excludes both endpoints (3 < x < 7), while [3, 7] includes both (3 ≤ x ≤ 7). You can also mix: [3, 7) includes 3 but excludes 7.
No! Infinity is not a number, so it can never be included. Always use parentheses with ∞: (-∞, 5) or (3, ∞), never [-∞, 5] or [3, ∞].
The ∪ symbol means "union" and combines two intervals. It represents OR in logic: (-∞, 2) ∪ (5, ∞) means x < 2 OR x > 5.
A single number is written as [a, a]. For example, [5, 5] represents just the number 5. However, this is rarely used in practice.
Set-builder notation uses set notation: {x | x < 5} means "the set of all x such that x is less than 5." It's equivalent to (-∞, 5) in interval notation.
No! The left number must be smaller than the right number. (7, 3) is invalid; you would write (3, 7) instead.
All real numbers are represented as (-∞, ∞), which corresponds to the inequality statement that x can be any real number.