# Bracket (mathematics)

**Bracketsbracketorderparenthesesparenthesize**

In mathematics, various typographical forms of brackets are frequently used in mathematical notation such as parentheses, square brackets [ ], braces { }, and angle brackets ⟨ ⟩.wikipedia

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### Expression (mathematics)

**expressionmathematical expressionexpressions**

Also in mathematical expressions in general, parentheses are used to indicate grouping (that is, which parts belong together) when necessary to avoid ambiguities, or for the sake of clarity.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations, and other aspects of logical syntax.

### Christopher Clavius

**ClaviusChristoph ClaviusChristof Klau**

The earliest use of brackets to indicate aggregation (i.e. grouping) was suggested in 1608 by Christopher Clavius and in 1629 by Albert Girard.

### Mathematics

**mathematicalmathmathematician**

In mathematics, various typographical forms of brackets are frequently used in mathematical notation such as parentheses, square brackets [ ], braces { }, and angle brackets ⟨ ⟩.

### Mathematical notation

**notationmathematical formulaealgebraic notation**

In mathematics, various typographical forms of brackets are frequently used in mathematical notation such as parentheses, square brackets [ ], braces { }, and angle brackets ⟨ ⟩.

### Bracket

**parentheses{brackets**

In mathematics, various typographical forms of brackets are frequently used in mathematical notation such as parentheses, square brackets [ ], braces { }, and angle brackets ⟨ ⟩.

### Vinculum (symbol)

**vinculum**

Historically, other notations, such as the vinculum, were similarly used for grouping; in present-day use, these notations all have specific meanings.

### Albert Girard

**GirardGirard, Albert**

The earliest use of brackets to indicate aggregation (i.e. grouping) was suggested in 1608 by Christopher Clavius and in 1629 by Albert Girard.

### ASCII

**US-ASCIIAmerican Standard Code for Information InterchangeASCII code**

### Unicode

**Unicode StandardUnicode Transformation FormatThe Unicode Standard**

### LaTeX

**LaTeX2HTMLHlineLaTeX2e**

In LaTeX the markup is and :.

### Elementary algebra

**Algebraelementary formElementary**

In elementary algebra parentheses, are used to specify the order of operations.

### Order of operations

**precedenceoperator precedencePrecedence of operators**

In elementary algebra parentheses, are used to specify the order of operations.

### Algebra

**algebraicAlgebra IAlgebra 1**

This notation is extended to cover more general algebra involving variables: for example

### Natural transformation

**natural isomorphismnaturalnaturally isomorphic**

For example, in the formula X = ε Cod η X η X, used in the definition of composition of two natural transformations, the parentheses around εη serve to indicate that the indexing by X is applied to the composition εη, and not just its last component η.

### Function (mathematics)

**functionfunctionsmathematical function**

The arguments to a function are frequently surrounded by brackets: f(x).

### Cartesian coordinate system

**Cartesian coordinatesCartesian coordinateCartesian**

In the cartesian coordinate system brackets are used to specify the coordinates of a point: (2,3) denotes the point with x-coordinate 2 and y-coordinate 3.

### Inner product space

**inner productinner-product spaceinner products**

The inner product of two vectors is commonly written as, but the notation (a, b) is also used.

### Interval (mathematics)

**intervalopen intervalclosed interval**

Both parentheses, and square brackets, [ ], can also be used to denote an interval.

### Finite set

**finitefinitelyfinite sets**

The numbers may come as close as they like to 12, including 11.999 and so forth (with any finite number of 9s), but 12.0 is not included.

### Infinity

**infiniteinfinitely∞**

Whenever infinity or negative infinity is used as an endpoint in the case of intervals on the real number line, it is always considered open and adjoined to a parenthesis.

### Extended real number line

**extended real numbersextended real line+∞**

The endpoint can be closed when considering intervals on the extended real number line.

### Set (mathematics)

**setsetsmathematical set**

Braces { } are used to identify the elements of a set: {a,b,c} denotes a set of three elements.

### Group theory

**groupgroup theoreticalgroup-theoretic**

Angle brackets are used in group theory to write group presentations, and to denote the subgroup generated by a collection of elements.

### Presentation of a group

**presentationfinitely presented groupgroup presentation**

Angle brackets are used in group theory to write group presentations, and to denote the subgroup generated by a collection of elements.

### Generating set of a group

**generatedgeneratorsgenerator**

Angle brackets are used in group theory to write group presentations, and to denote the subgroup generated by a collection of elements.