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3.10.4 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

Operators used in calculus.

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.

xy and xy are both taken to give the built-in function Implies[x, y]. xy gives the built-in function Element[x, y].

This is interpreted using the built-in functions And and Implies.

In[1]:= 3 < 4 And x > 5 Implies y < 7


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 .



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 above 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.

In[1]:= x CirclePlus y Cap z // FullForm


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.

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.

In[1]:= {a == b, a Equal b, a != b, a NotEqual b}


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 ->.

In[1]:= x + y /. x Rule 3


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.

In[2]:= x Equilibrium y UpEquilibrium z