One or both of the square bracket symbols [ and ] are used in many different contexts in mathematics.

1. Square brackets are occasionally used in especially complex expressions in place of (or in addition to) parentheses, especially as a group symbol outside an inner set of parentheses, e.g., .

2. Large brackets around an array of numbers, e.g., indicate a matrix. (The symbol is also commonly used.)

3. A square bracket at one end of an interval indicates that the interval is closed at that end (i.e., the number adjacent to the opening or closing square bracket is included in the interval).

4. A simple continued fraction with partial denominators , , ... is sometimes denoted .

5. Brackets may be used to denote the least common multiple, e.g., .

6. Some sources (of which this work is not one) use to denote the floor function .

7. Gaussian brackets notation represents a combination of simple continued fraction partial denominators that is not equivalent to the continued fraction itself (but which is a related quantity that can be useful for computing continued fractions recursively from the partial denominators).

See also

Angle Bracket, Brace, Bracket, Closed Interval, Half-Closed Interval, Interval, Parenthesis, Simple Continued Fraction

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References

Bringhurst, R. The Elements of Typographic Style, 2nd ed. Point Roberts, WA: Hartley and Marks, p. 285, 1997.Grossman, J. (Managing Ed.). "Brackets." §5.128-5.132 in The Chicago Manual of Style, 14th ed. Chicago, IL: University of Chicago Press, pp. 190-191, 1993.

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Square Bracket

Cite this as:

Weisstein, Eric W. "Square Bracket." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SquareBracket.html

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