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...ity''' is a property of [[binary operation]]s. If <math>\star</math> is a binary operation then the associative property is the condition that

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In [[algebra]], '''distributivity''' is a property of two [[binary operation]]s which generalises the relationship between [[addition]] and [[multiplica

In the common case of a [[binary operation]] <math>\star</math>, written now in [[operator notation]], we can write

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...that F is a commutative group with an [[identity element]] 0; and another binary operation ''*'' on F such that F\{0} is a commutative group with identity element 1. The first binary operation is usually called ''addition'' and the second one ''multiplication''.

* [[Identity element]], or neutral element, with respect to a binary operation, an element which leaves the other operand unchanged.

'''Multiplication''' is the [[binary operation|binary]] [[operation (mathematics)|mathematical operation]] of scaling one Multiplication may also be used to describe more general [[binary operation]]s.

An adder performs a binary operation (two operands) where the ''n'' of one power in integer ''A'' is added to th

# There is a [[commutative operation|commutative]] binary operation, called ''addition'' (denoted by +) and the field ℝ is closed under this # There is a commutative binary operation, called ''multiplication'' (denoted by &times;) and the field ℝ is closed

Let ''M'' be a set with a [[binary operation]] <math>\circ</math> and ''R'' a [[ring (mathematics)|ring]]. Let ''f'' an

In [[algebra]], '''absorption''' is a property of [[binary operation]]s which reflects an underlying [[order (relation)|order relation]].

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...\{\dots, -2, -1, 0, 1, 2, \dots\}</math> together with the constant 0, the binary operation <math>+</math> (addition), the unary function <math>-</math> (which maps ea

...e sequences, over the "alphabet" <math>X \cup \bar X</math> and take the [[binary operation]] of concatenation (juxtaposition) of words. The [[identity element]] for

...detailed below. For example, the set of integers with ''addition'' as the binary operation is a group. [[Group theory]] is the branch of mathematics which studies gro * ''[[closure (binary operation)|Closure]]'': For all ''a'' and ''b'' in ''G'', ''a'' * ''b'' belongs to ''

...operation]]s''': The notion of [[addition]] (+) is abstracted to give a ''binary operation'', * say. For two elements ''a'' and ''b'' in a set ''S'' ''a''*''b'' gives ...dition and one is the identity element for multiplication. For a general [[binary operation]] * the identity element ''e'' must satisfy ''a'' * ''e'' = ''a'' and ''e''

but as a [[mathematical symbol]] for a binary operation (such as the plus sign "+")

A '''ring''' is a [[set]] ''R'' equipped with two [[binary operation]]s, which are generally denoted + and · and called ''addition'' and ''mult

Maximum and minimum are [[binary operation]]s on a linearly ordered set, sometimes written <math>x \vee y</math> and <

...[[algebra]] <math>\scriptstyle\mathbb{A}</math> which is equipped with the binary operation of "+" ([[addition]]) and a [[topological space|topology]], for example the

A '''group''' is a [[set (mathematics)|set]] <math>G</math> and a [[binary operation]] <math>\cdot</math> that has the following properties:

Addition is a binary operation <math>\;+\;</math> in <math>\mathbb N</math> Multiplication is a binary operation <math>\;\cdot\;</math> in <math>\mathbb N</math>

...}</math>. This means that even though addition is strictly defined as a [[binary operation]], the object <math>\vec{u}+\vec{v}+\vec{w}</math> is well defined.

Like the natural numbers, '''Z''' is closed below the [[binary operation|operations]] of [[addition]] and [[multiplication]], that is, the sum and p

Informally, the right fold applies to a binary operation (say, "+"), a list (say, "[''x'',''y'',''z'']") and an initial value (say,