# 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].

x×y | Times[x,y] | multiplication |

x÷y | Divide[x,y] | division |

√x | Sqrt[x] | square root |

xy | Cross[x,y] | vector cross product |

±x | PlusMinus[x] | (no built-in meaning) |

x±y | PlusMinus[x,y] | (no built-in meaning) |

x | MinusPlus[x] | (no built-in meaning) |

xy | MinusPlus[x,y] | (no built-in meaning) |

Interpretation of some operators in basic arithmetic and algebra.

## Operators in Calculus and Algebra

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[x, y]. gives the built-in function Element[x, y].

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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.

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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.

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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.

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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.

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

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