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- In [[mathematics]], a '''binary operation''' on a set is a function of two variables which assigns a value to any pai Formally, a binary operation <math>\star</math> on a set ''S'' is a function on the [[Cartesian product]1 KB (202 words) - 12:53, 12 December 2008
- 162 bytes (24 words) - 12:45, 28 November 2008
- 304 bytes (41 words) - 13:19, 6 December 2008
Page text matches
- The [[binary operation|binary]] [[operation (mathematics)|mathematical operation]] of scaling one178 bytes (20 words) - 17:37, 28 March 2009
- In [[algebra]], an '''idempotent element''' with respect to a [[binary operation]] is an element which is unchanged when combined with itself. Formally, let <math>\star</math> be a binary operation on a set ''X''. An element ''E'' of ''X'' is an idempotent for <math>\star1,007 bytes (146 words) - 16:14, 13 December 2008
- In [[mathematics]], a '''binary operation''' on a set is a function of two variables which assigns a value to any pai Formally, a binary operation <math>\star</math> on a set ''S'' is a function on the [[Cartesian product]1 KB (202 words) - 12:53, 12 December 2008
- For [[binary operation]]s, an element that has one of two properties analoguous to the number zero136 bytes (20 words) - 19:29, 10 November 2009
- An algebraic structure with an associative binary operation.96 bytes (11 words) - 02:19, 9 November 2008
- * For an additively written binary operation, ''z'' is a ''zero element'' if (for all ''g'') * For a multiplicatively written binary operation, ''a'' is a ''zero element'' if (for all ''g'')853 bytes (133 words) - 19:23, 10 November 2009
- An element whose behaviour with respect to a binary operation generalises that of zero for addition or one for multiplication.162 bytes (23 words) - 02:15, 6 December 2008
- An algebraic structure with an associative binary operation and an identity element.120 bytes (15 words) - 02:21, 9 November 2008
- A property of a binary operation (such as addition or multiplication), that the two operands may be intercha178 bytes (25 words) - 06:20, 6 December 2008
- An element whose behaviour with respect to an algebraic binary operation is like that of zero with respect to multiplication.161 bytes (23 words) - 02:25, 5 December 2008
- ...[[operator (mathematics)|operator]]s on a set. If <math>\star</math> is a binary operation then the commutative property is the condition that695 bytes (102 words) - 19:40, 31 January 2009
- In [[algebra]], a '''semigroup''' is a set equipped with a binary operation satisfying certain properties similar to but less stringent than those of a Formally, a semigroup is a set ''S'' with a binary operation <math>\star</math> satisfying the following conditions:3 KB (405 words) - 16:21, 13 November 2008
- In [[algebra]], an '''absorbing element''' or a '''zero element''' for a [[binary operation]] has a property similar to that of [[multiplication]] by [[zero]]. Formally, let <math>\star</math> be a binary operation on a set ''X''. An element ''O'' of ''X'' is absorbing for <math>\star</ma726 bytes (112 words) - 15:21, 21 December 2008
- {{r|Binary operation}}243 bytes (26 words) - 13:20, 6 December 2008
- ...]], an '''identity element''' or '''neutral element''' with respect to a [[binary operation]] is an element which leaves the other operand unchanged, generalising the Formally, let <math>\star</math> be a binary operation on a set ''X''. An element ''I'' of ''X'' is an identity for <math>\star</927 bytes (140 words) - 15:33, 8 December 2008
- {{r|Binary operation}}174 bytes (20 words) - 04:26, 18 January 2010
- A [[binary operation]] <math>\star</math> is ''idempotent'' if2 KB (242 words) - 13:20, 18 November 2022
- In [[algebra]], a '''monoid''' is a set equipped with a binary operation satisfying certain properties similar to but less stringent than those of a Formally, a monoid is set ''M'' with a binary operation <math>\star</math> satisfying the following conditions:3 KB (526 words) - 11:02, 23 December 2008
- ...'' is the set of 3×3 [[self-adjoint]] matrices over the [[octonion]]s with binary operation619 bytes (88 words) - 13:53, 14 November 2008
- ...arguments it takes. In the case of real number addition, the operator is [[binary operation|binary]] because it takes two arguments.617 bytes (102 words) - 13:04, 12 December 2008
- ...ity''' is a property of [[binary operation]]s. If <math>\star</math> is a binary operation then the associative property is the condition that2 KB (295 words) - 14:56, 12 December 2008
- {{r|Binary operation}}902 bytes (142 words) - 14:48, 23 December 2008
- In [[algebra]], '''distributivity''' is a property of two [[binary operation]]s which generalises the relationship between [[addition]] and [[multiplica2 KB (226 words) - 13:15, 18 November 2022
- In the common case of a [[binary operation]] <math>\star</math>, written now in [[operator notation]], we can write1,002 bytes (157 words) - 13:37, 8 March 2009
- {{r|Binary operation}}969 bytes (124 words) - 18:42, 11 January 2010
- {{r|Binary operation}}200 bytes (22 words) - 10:02, 12 November 2009
- {{r|Binary operation}}948 bytes (147 words) - 14:57, 6 December 2008
- ...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''.3 KB (496 words) - 22:16, 7 February 2010
- * [[Identity element]], or neutral element, with respect to a binary operation, an element which leaves the other operand unchanged.591 bytes (78 words) - 12:52, 31 May 2009
- '''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.5 KB (638 words) - 14:16, 17 December 2008
- An adder performs a binary operation (two operands) where the ''n'' of one power in integer ''A'' is added to th2 KB (368 words) - 05:19, 17 March 2024
- # 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 ×) and the field ℝ is closed4 KB (562 words) - 18:28, 5 January 2010
- Let ''M'' be a set with a [[binary operation]] <math>\circ</math> and ''R'' a [[ring (mathematics)|ring]]. Let ''f'' an2 KB (338 words) - 17:41, 23 December 2008
- In [[algebra]], '''absorption''' is a property of [[binary operation]]s which reflects an underlying [[order (relation)|order relation]].929 bytes (125 words) - 13:24, 18 November 2022
- {{r|Binary operation}}850 bytes (136 words) - 15:22, 21 December 2008
- {{r|Binary operation}}850 bytes (136 words) - 15:37, 8 December 2008
- {{r|Binary operation}}850 bytes (136 words) - 15:05, 12 December 2008
- {{r|Binary operation}}870 bytes (138 words) - 14:59, 12 December 2008
- ...\{\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 ea2 KB (348 words) - 16:37, 10 March 2009
- ...e sequences, over the "alphabet" <math>X \cup \bar X</math> and take the [[binary operation]] of concatenation (juxtaposition) of words. The [[identity element]] for2 KB (436 words) - 02:56, 15 November 2008
- ...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 ''19 KB (3,074 words) - 11:11, 13 February 2009
- ...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''18 KB (2,669 words) - 08:38, 17 April 2024
- but as a [[mathematical symbol]] for a binary operation (such as the plus sign "+")3 KB (422 words) - 09:31, 22 April 2014
- A '''ring''' is a [[set]] ''R'' equipped with two [[binary operation]]s, which are generally denoted + and · and called ''addition'' and ''mult10 KB (1,667 words) - 13:47, 5 June 2011
- Maximum and minimum are [[binary operation]]s on a linearly ordered set, sometimes written <math>x \vee y</math> and <3 KB (538 words) - 18:17, 17 January 2010
- ...[[algebra]] <math>\scriptstyle\mathbb{A}</math> which is equipped with the binary operation of "+" ([[addition]]) and a [[topological space|topology]], for example the4 KB (604 words) - 05:50, 12 May 2008
- A '''group''' is a [[set (mathematics)|set]] <math>G</math> and a [[binary operation]] <math>\cdot</math> that has the following properties:15 KB (2,535 words) - 20:29, 14 February 2010
- 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>16 KB (2,562 words) - 00:45, 13 October 2009
- ...}</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.15 KB (2,506 words) - 05:16, 11 May 2011
- Like the natural numbers, '''Z''' is closed below the [[binary operation|operations]] of [[addition]] and [[multiplication]], that is, the sum and p10 KB (1,566 words) - 08:34, 2 March 2024
- Informally, the right fold applies to a binary operation (say, "+"), a list (say, "[''x'',''y'',''z'']") and an initial value (say,21 KB (3,291 words) - 16:07, 3 November 2013