How to Type Interval Notation on DeltaMath (Parentheses, Brackets, Union & Infinity)
The short version
Use parentheses ( ) for strict inequalities (< or >), brackets [ ] for inclusive inequalities (≤ or ≥), and always type infinity — never the ∞ symbol. Infinity always gets a parenthesis, never a bracket. For compound inequalities with two separate intervals, join them with an uppercase U.
The Exact Syntax DeltaMath Expects
DeltaMath accepts interval notation typed directly into the answer box. The system checks your entry character by character, so a bracket in the wrong position or the ∞ symbol instead of the word “infinity” will mark a mathematically correct answer wrong.
Parentheses vs brackets
The rule maps directly from the inequality symbol:
Parenthesis ( ) — open endpoint
Used when the endpoint is not included. Inequality uses < or >. Examples: x > 3 → (3, infinity)
Bracket [ ] — closed endpoint
Used when the endpoint is included. Inequality uses ≤ or ≥. Examples: x ≥ 3 → [3, infinity)
Infinity entry
Type the word infinity — all lowercase, no spaces. DeltaMath does not reliably accept the ∞ symbol when typed from a keyboard or pasted from another source. For negative infinity, type -infinity. Infinity is never included in an interval, so it always takes a parenthesis: (3, infinity) not (3, infinity].
Union notation for compound inequalities
When a solution has two separate pieces — for example, x < −2 or x ≥ 4 — join the intervals with an uppercase U. Type the complete entry as: (-infinity, -2) U [4, infinity). The on-screen keyboard in DeltaMath includes a union button for problems that expect it — use the button if it’s available; it produces the correct character. A lowercase u is not accepted.
List the left interval first (the one with −infinity). DeltaMath expects intervals written in order from left to right on the number line. Reversing the order may be marked incorrect.
All real numbers
When every real number is a solution — for example, x > −5 OR x < 10, which has no gap anywhere on the number line — the interval notation entry is (-infinity, infinity). Do not type Infinite Solutions here. “Infinite Solutions” is a valid DeltaMath entry for equations (like 2x = 2x, which is true for every x), but inequality problems asking for interval notation expect the actual interval written out: (-infinity, infinity).
No solution
If the inequality has no solution — for example, x < 2 AND x > 5, which has no overlap — do not enter an empty set symbol. Type No Solution with a capital N and capital S, no punctuation. See the full breakdown at How to Enter No Solution on DeltaMath.
Does spacing after the comma matter?
No. DeltaMath’s parser ignores whitespace inside interval notation. (3, infinity) and (3,infinity) are treated identically. You do not need to worry about adding or removing a space after the comma — that is one formatting detail that will not cost you points.
Interval Notation Reference Card
The table below shows the correct DeltaMath entry for the most common interval types, alongside what students commonly type that gets marked wrong.
Interval notation reference card for DeltaMath — parentheses, brackets, union, and infinity rules
Four Mistakes That Cost Points
1. Bracket next to infinity
The most common error. Typing [3, infinity] instead of [3, infinity). Infinity cannot be “reached” or included, so the bracket next to it is always a parenthesis. There are no exceptions.
2. Using the ∞ symbol instead of the word
Copying and pasting the ∞ character from another source, or using the symbol directly from a phone keyboard, often produces a character that DeltaMath’s parser does not recognize. Type infinity as a word. If the on-screen keyboard has an ∞ button, use that button — it inserts the correct internal character. Don’t copy-paste the symbol from elsewhere.
3. Lowercase u for union
DeltaMath requires an uppercase U for the union symbol. Typing a lowercase u, or writing the word “or” between the intervals, will be rejected. If the problem provides a union button on the on-screen keyboard, use it rather than typing the letter.
4. Reversing the interval order on a union
DeltaMath expects intervals in ascending order left to right on the number line. For x < −2 or x ≥ 4, write (-infinity, -2) U [4, infinity) — not [4, infinity) U (-infinity, -2). The mathematically equivalent reversed form is marked incorrect.
Interval notation problems in algebra and precalculus also require that you fully simplify before entering your answer. If you solved the inequality and got x ≤ 8/4, enter (-infinity, 2] — not (-infinity, 8/4]. For fraction simplification help see How to Enter Fractions in DeltaMath.
Formatting Rules by Problem Type
The bracket vs parenthesis choice isn’t the same for every problem type. Here’s what to expect in the most common contexts:
Absolute value inequalities
|x| < a → single interval, both endpoints open: (-a, a).
|x| > a → union of two open intervals: (-infinity, -a) U (a, infinity). Both sides use parentheses since the inequality is strict.
Domain and range
Polynomial functions: domain is always (-infinity, infinity). Radical functions (even roots): domain starts at the boundary value with a bracket. Rational functions: domain excludes undefined points — use a union with parentheses at each excluded value.
Increasing / decreasing intervals
Always parentheses only — no brackets. A function is increasing between turning points, not at them. Even if the endpoint is in the domain, it is excluded from the increasing/decreasing interval: (2, 7) not [2, 7].
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