Operation (mathematics)

In mathematics linkage is used as a generic term to next various arithmetic arithmetic operations ( such as addition, subtraction, etc.) and geometric operations (such as mirroring, rotation, and others) and other (sometimes logical ) take operations. A link defines how mathematical objects of the same or similar nature are interconnected. With a relatively small number of elements and a link with only a few such as two points at which items can be as operands, this determination is clearly by a truth table possible in the link, for example, for a 2-digit all possible pairings are listed and their respective result is specified, the result of calculation.

The link word is also used to denote the sequential execution, or concatenation of functions.

• 3.1 Examples

General definition

For a natural number sets and a further quantity are given. Then every mapping of the Cartesian product is denoted by as - digit shortcut. Such a link so assigns each tuple with clearly an element of the set. Of course, the amounts and partially or completely match.

In the special case that only happens, ie, the link

Inner - digit shortcut or digits operation on called. If at least one time under the front, about

For one with so called linking outer - digit shortcut on with operator domain. The elements of are then called operators.

An inner - digit shortcut you can also serve as external binary operation to consider the operator domain.

Example

The through

Defined mapping from to is a three-digit combination and inner three-digit shortcut.

Is a picture of the rebound is due to

An external binary operation given on with operator domain and the single operator.

Each digit combination can be thought of as - place relation.

Zero digit shortcuts

As a zero -digit combination of a quantity of a quantity can be considered a mapping from to. It is

Therefore you can choose any of these images indicated as follows:

Each zero binary operation is thus constant and can be regarded as the constant turn.

As always applies, any zero digit combination can be considered as inner join on:

Digit links

Digit links are pictures of a lot like a lot.

Examples

• Given a set. For each element of the power set, ie, for each subset of, is defined:

• The sine function

Two-digit ( binary ) links

Most frequently, the term " link " is used in the sense of a two -digit shortcut. Important special cases are internal and external links. Two-digit shortcuts are often quoted in infix notation, ie by a standing between the two operands symbol such as a plus sign.

Three - and multi-digit shortcuts

Rarely, one speaks of three - and multi-digit shortcuts. Examples of a three-digit combination are:

• The picture from the triple product assigns her three vectors (off) and
• The Ternärverknüpfung in a Ternärkörper.

Links in the algebra

Links serve in algebra to define algebraic structures. The links must meet certain conditions ( axioms ).

For example, a semigroup is a set with an inner double-digit combination that satisfies the associative law. The requirement that the result of the link again to be an element of the given set ( seclusion ) is already included in the definition of the inner join.