Definition:Operation/Arity

Definition
The arity of an operator is the number of operands it uses.

An alternative (older) term is valency.

The arity of an operator may be, in general, any number.

Unary
A unary operator (or one-place operator) is an operator which takes one operand, that is, its arity is $$1$$.

An example of a unary operator from arithmetic is $$\sqrt{}$$ (i.e. the square root sign).

Binary
A binary operator (or two-place operator) is an operator which takes two operands, that is, its arity is $$2$$.

Ternary
A ternary operator (or three-place operator) is an operator which takes three operands, that is, its arity is $$3$$.

And so on.

n-ary
Certain types of operator have a fixed number of operands. An operator with $$n$$ operands is sometimes called an "$$n$$-ary operator".

Multiary
Certain other types of operator have a variable number of operands. An operator which does not have a fixed arity is called multiary or multigrade.

Finitary
A finitary operator is one which takes a finite number of operands.

Arity of Zero
It is possible to conceive of an operator which takes no operands.

A constant can be considered as an operator which takes no operands, and there are circumstances in mathematics and logic in which it is advantageous to do so.