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- In [[mathematics]], the '''Cartesian product''' of two sets ''X'' and ''Y'' is the set of [[ordered pair]]s from ''X'' a The Cartesian product has a [[universal property]]: if there is a set ''Z'' with maps <math>f:Z \3 KB (440 words) - 12:26, 30 December 2008
- 101 bytes (15 words) - 02:33, 3 November 2008
- 649 bytes (78 words) - 17:30, 3 November 2008
- 927 bytes (149 words) - 02:35, 3 November 2008
Page text matches
- #REDIRECT [[Cartesian product#Cartesian power]]47 bytes (5 words) - 12:58, 12 December 2008
- The Cartesian product of compact topological spaces is compact.99 bytes (12 words) - 05:27, 29 December 2008
- A function which maps some finite Cartesian product of a set to itself.107 bytes (16 words) - 15:18, 20 May 2008
- In [[mathematics]], the '''Cartesian product''' of two sets ''X'' and ''Y'' is the set of [[ordered pair]]s from ''X'' a The Cartesian product has a [[universal property]]: if there is a set ''Z'' with maps <math>f:Z \3 KB (440 words) - 12:26, 30 December 2008
- ...ology]], the '''product topology''' is an assignment of open sets to the [[Cartesian product]] of a family of [[topological space]]s. By iteration, the product topology on a finite Cartesian product ''X''<sub>1</sub>×...×''X''<sub>''n''</sub> is the topology with sub-basi2 KB (345 words) - 16:47, 6 February 2010
- {{r|Cartesian product}}592 bytes (77 words) - 19:15, 11 January 2010
- A closely related formulation of the axiom is that the [[Cartesian product]] of any family of non-empty sets is again non-empty.2 KB (266 words) - 13:28, 5 January 2013
- An [[infinite set|infinite]] [[Cartesian product]] of non-empty non-[[compact space]]s has the property that every compact s850 bytes (118 words) - 22:30, 20 February 2010
- ...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
- {{r|Cartesian product}}1 KB (187 words) - 19:18, 11 January 2010
- * The [[Cartesian product]] of two (and hence finitely many) compact spaces with the [[product topolo4 KB (652 words) - 14:44, 30 December 2008
- ...rdered pairs (''x'',''y'') with ''x'' in ''X'' and ''y'' in ''Y'' is the [[Cartesian product]] of ''X'' and ''Y''. A [[complex number]] may be expressed as an ordered1 KB (213 words) - 07:01, 21 January 2009
- ...''binary relation''' between sets ''X'' and ''Y'' as a [[subset]] of the [[Cartesian product]], <math>R \subseteq X \times Y</math>. We write <math>x~R~y</math> to ind4 KB (684 words) - 11:25, 31 December 2008
- ..., but is clearly associated with it. (Formally it is a bilinear map of the Cartesian product ℝ<sup>3</sup>×ℝ<sup>3</sup> into ℝ). The inner product satisfie9 KB (1,373 words) - 06:21, 11 December 2009
- ...uct (ring theory)|direct product]]'' of two rings ''R'' and ''S'' is the [[cartesian product]] ''R''×''S'' together with the operations10 KB (1,667 words) - 13:47, 5 June 2011
- ...ample, arithmetic has the product of a pair of numbers, set theory has the Cartesian product of a pair of sets and logic has the conjunction of a pair of assertions. T7 KB (1,151 words) - 14:44, 26 December 2013
- : The [[Cartesian product]] of finitely many countable sets is countable. that the Cartesian product of two countable sets is countable.10 KB (1,462 words) - 17:24, 25 August 2013
- : The [[Cartesian product]] of finitely many countable sets is countable. that the Cartesian product of two countable sets is countable.10 KB (1,462 words) - 17:25, 25 August 2013
- Formally, a group action is a map from the [[Cartesian product]] <math>G \times X \rightarrow X</math>,4 KB (727 words) - 12:37, 16 November 2008
- The '''Cartesian product''' or '''direct product''' of two sets ''A'' and ''B'' is the set defined b17 KB (2,828 words) - 10:37, 24 July 2011
- ...also be defined with any number of terms, finite or infinite, by using the cartesian product and defining the operation coordinate-wise.19 KB (3,074 words) - 11:11, 13 February 2009
- ...morphic at a point if it is locally expandable (within a [[polydisk]], a [[cartesian product]] of [[disk (mathematics)|disk]]s, centered at that point) as a convergent9 KB (1,434 words) - 15:35, 7 February 2009
- ...\ \pi_a : X \rightarrow X_a</math> be the standard projection of the cartesian product ...niformity <math>\mathcal U</math> (see above) is the only one in the Cartesian product <math>\ X</math>, which satisfies the following two conditions:45 KB (7,747 words) - 06:00, 17 October 2013
- ...bability distribution is then a subset T={(s0,t0),...,(sn,tn), ...} of the cartesian product <math>S \times A</math>, such that all the ti sum to exactly 1.4 KB (590 words) - 09:17, 26 September 2007
- ...is a family of topological spaces, then the ''product topology'' on the [[Cartesian product]] <math>\prod_{\lambda\in\Lambda} X_\lambda</math> has as sub-basis the set15 KB (2,586 words) - 16:07, 4 January 2013
- ...''A'' is an affine space of dimension ''n'' if there exists a map of the [[Cartesian product]], ''A'' × ''A'' onto a vector space of dimension ''n''. This map mus15 KB (2,366 words) - 09:09, 4 April 2010
- ...r <math>\vec{u}+\vec{v}</math>. Here <math>\times</math> represents the [[Cartesian product]] between sets. Scalar multiplication is defined in a similar way, as a ma15 KB (2,506 words) - 05:16, 11 May 2011
- ...n the FROM clause are retrieved. If more than one table is specified, the Cartesian product of the rows is produced. Next, the rows not satisfying the predicates prov6 KB (966 words) - 13:13, 18 February 2021
- Similarly 5 × 4 is the size of the [[Cartesian product]] of a set of size 5 with one of size 4. We define in general:11 KB (1,808 words) - 17:50, 26 June 2009
- ...n]]. A ''relation'' between sets ''X'' and ''Y'' is a [[subset]] of the [[Cartesian product]], <math>R \subseteq X \times Y</math>. We say that a relation ''R'' is ''15 KB (2,342 words) - 06:26, 30 November 2011