# Operators

## Basic Mathematical Operators

Some operators used in basic arithmetic and algebra.

Note that the

for

\[Cross] is distinguished by being drawn slightly smaller than the

for

\[Times].

Interpretation of some operators in basic arithmetic and algebra.

## Operators in Calculus and Algebra

Operators used in calculus.

Operators for complex numbers and matrices.

## Logical and Other Connectives

Operators used as logical connectives.

The operators

,

, and

are interpreted as corresponding to the built-in functions

And,

Or, and

Not, and are equivalent to the keyboard operators

,

, and

. The operators

,

, and

correspond to the built-in functions

Xor,

Nand, and

Nor. Note that

is a prefix operator.

and

are both taken to give the built-in function

Implies.

gives the built-in function

Element.

This is interpreted using the built-in functions

And and

Implies.

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*Mathematica* supports most of the standard syntax used in mathematical logic. In

*Mathematica*, however, the variables that appear in the quantifiers

,

, and

must appear as subscripts. If they appeared directly after the quantifier symbols then there could be a conflict with multiplication operations.

and

are essentially prefix operators like

.

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## Operators Used to Represent Actions

Operators typically used to represent actions. All the operators except \[Square] are infix.

Following

*Mathematica*'s usual convention, all the operators in the table are interpreted to give functions whose names are exactly the names of the characters that appear in the operators.

The operators are interpreted as functions with corresponding names.

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All the operators in the table above, except for

, are infix, so that they must appear in between their operands.

## Bracketing Operators

Characters used as bracketing operators.

x | Floor[x] |

x | Ceiling[x] |

mi,j,... | Part[m,i,j,...] |

x,y,... | AngleBracket[x,y,...] |

x,y,... | BracketingBar[x,y,...] |

x,y,... | DoubleBracketingBar[x,y,...] |

Interpretations of bracketing operators.

## Operators Used to Represent Relations

Operators usually used to represent similarity or equivalence.

The special character

(or

\[Equal]) is an alternative input form for

.

is used both for input and output.

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Operators usually used for ordering by magnitude.

Operators used for relations in sets.

Operators usually used for other kinds of orderings.

Relational operators based on vertical bars.

## Operators Based on Arrows and Vectors

Operators based on arrows are often used in pure mathematics and elsewhere to represent various kinds of transformations or changes.

is equivalent to

.

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Arrow-like operators with built-in meanings in *Mathematica*.

Ordinary arrows.

Vectors and related arrows.

All the arrow and vector-like operators in

*Mathematica* are infix.

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Tees.