Search results

[[File:Binary operations as black box.svg|thumb|A binary operation <math>\circ</math> is a rule for combining the arguments <math>x< ...e formally, a binary operation is an [[Operation (mathematics)|operation]] of [[arity]] two. ...

{{Short description|Property of a binary operation}} ...m+n}</math> for all positive integers <math>m, n</math>. It is a weak form of [[associativity]]. ...

{{Short description|Specific element of an algebraic structure}} ...is no possibility of confusion, but the identity implicitly depends on the binary operation it is associated with. ...

{{Short description|Mathematical set of all subsets of a set}} | image = Hasse diagram of powerset of 3.svg ...

.../csharp_color_image_to_binary.aspx |title=Conversion of a Color Image to a Binary Image |publisher=CoderSource.net |date=2005-04-18 |access-date=2008-06-11 | ...ge''' is a [[digital image]] that consists of [[pixels]] that can have one of exactly two colors, usually black and white. Each pixel is stored as a sing ...

{{short description|Set of elements in any of some sets}} [[File:Venn0111.svg|thumb|200px|Union of two sets:<br /><math>~A \cup B</math>]] ...

{{Short description|Set of the elements not in a given subset}} ...red inside a square. The area outside the circle is unfilled. The borders of both the circle and the square are black. ...

[[File:Venn 0000 0001.svg|220px|thumb|[[Venn diagram]] of <math>A \wedge B \land C</math>]] ...'''conjunction''' or '''logical conjunction'''. The [[logical connective]] of this operator is typically represented as <math>\wedge</math><ref name=":2" ...

{{Short description|Property involving two mathematical operations}} | image = [[File:Illustration of distributive property with rectangles.svg|300px|class=skin-invert-image]] ...

{{Short description|Property of a mathematical operation}} | image = [[File:Associativity of binary operations (without question marks).svg|300px|class=skin-invert-image]] ...

{{Short description|Rooted binary tree data structure}} |name=Binary search tree ...

{{Short description|Limited form of tree data structure}} {{Distinguish|Binary search tree|B-tree|B+ tree}} ...

==Structures and operations== * [[Direct product of groups]] ...

...s)|groups]]: A ''quasigroup'' is a [[magma (algebra)|magma]] with the type of [[Division (mathematics)#Abstract algebra|divisibility]] given by the [[Qua ...er from groups mainly in that the [[associative]] and [[identity element]] properties are optional. In fact, a [[Empty set|nonempty]] associative quasigroup is a ...

...nal arrays of numbers), their outer product is a tensor. The outer product of tensors is also referred to as their [[tensor product]], and can be used to ...[dot product]] (a special case of "[[inner product]]"), which takes a pair of coordinate vectors as input and produces a [[scalar (mathematics)|scalar]] ...

...bn=978-3-540-60275-0 }}</ref> It supports 'lookup', 'remove', and 'insert' operations. The '''dictionary problem''' is the classic problem of designing efficient [[data structure]]s that implement associative arrays.< ...

{{Short description|Variant of heap data structure}} | name = Binary (min) heap ...

{{short description|Concept that is not defined in terms of previously defined concepts}} ...eading. Formal theories cannot dispense with primitive notions, under pain of [[infinite regress]]. ...

...its elements that is compatible with the field operations. Basic examples of ordered fields are the [[Rational number|rational numbers]] and the [[real ...is implies that the [[complex number]]s cannot be ordered since the square of the [[imaginary unit]] ''i'' is {{num|−1}} (which is negative in any ordere ...

{{Short description|Generalization of additive and multiplicative inverses}} ...ath|−''x''}}) and [[Multiplicative inverse|reciprocal]] ({{math|1/''x''}}) of numbers. ...