# 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.