Operation

An operation is an infix form of some (very popular) functions. Usually, in the infix position, the name of the function is replaced with a custom symbol called operand; although some infix operands lack the symbolic form, e.g. $n\mod m \ \ \equiv \mod(n,m)$.

An operation is a calculation from (zero or more) input values, called operands, to an output value.

The number of operands is the arity of the operation.

The most commonly studied operations are binary operations, (operations of arity 2, such as addition, multiplication) and unary operations (factorial,additive inverse, negation).

An operation of arity zero, or nullary operation, is a constant.

The mixed product is an example of an operation of arity 3, also called ternary operation.

Generally, the arity is supposed to be finite. However, infinitary operations are sometimes considered, in which context the "usual" operations of finite arity are called finitary operations.

https://en.wikipedia.org/wiki/Operation_(mathematics) https://en.wikipedia.org/wiki/Operator_(mathematics)

• function

• operation

• operand

• operand arity

• operator(s)

The derived operand keeps the same arity as the function. There are operandsof other arity, but the prevalent are thebinary operators.

counterparts, operands may be $n$-ary (although prevalently binary).

A unary function like negation, $Neg(n)$, will correspondingly have unary operand, $-n$.

For example, the very popular addition function, $add(m,n)$, has the short, infix form as the operator $m+n$.

calculation that combines two elements (called operands) to produce another element.

A binary operation is an operation of arity two.

Elementary arithmetic operations are binary:

• addition: + plus (rarely used as unary operand)

• subtraction: − minus (may also be unary operand to change sign)

• division: ÷ obelus

• multiplication: × times

Binary operations

https://en.wikipedia.org/wiki/Binary_operation

A binary operation (dyadic operation) is a calculation that combines two elements (called operands) to produce another element. More formally, a binary operation is an operation of arity two.

More specifically, a binary operation on a set is a binary operation whose two domains and the codomain are the same set. Examples include the familiar arithmetic operations of addition, subtraction, multiplication. Other examples are readily found in different areas of mathematics, such as vector addition, matrix multiplication and conjugation in groups.

However, a binary operation may also involve several sets. For example, scalar multiplication of vector spaces takes a scalar and a vector to produce a vector, and scalar product takes two vectors to produce a scalar.

Binary operations are the keystone of most algebraic structures, that are studied in algebra, and used in all mathematics, such as fields, groups, monoids, rings, algebras, and many more.