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- '''Cardinality''' is the notion that answers the question "How many?", However, the concept of cardinality can be understood without having names for numbers,2 KB (347 words) - 18:14, 26 June 2009
- 105 bytes (16 words) - 16:06, 17 June 2009
- 12 bytes (1 word) - 18:26, 26 June 2009
- 91 bytes (11 words) - 18:29, 26 June 2009
Page text matches
- Sets of cardinality < 2.64 bytes (6 words) - 10:10, 4 December 2008
- Sets of cardinality < 2.64 bytes (6 words) - 10:05, 4 December 2008
- is the traditional notation for the [[cardinality]] of the set of [[natural number]]s. The ''cardinality of a set is aleph-0'' (or shorter,1 KB (214 words) - 13:35, 6 July 2009
- Cardinality (size) of the set of all natural numbers.89 bytes (12 words) - 05:39, 25 June 2008
- [http://carnot.yi.org/Category2.xhtml Category '''2''', sets of cardinality < 2.]<br/>99 bytes (14 words) - 23:21, 19 December 2008
- {{r|Cardinality|Order of a finite set or algebraic structure}}248 bytes (33 words) - 17:37, 14 April 2010
- For a group, its cardinality; for an element of a group, the least positive integer (if one exists) such199 bytes (32 words) - 17:17, 20 November 2008
- ...''124''' (1996) 2555-2560. Zbl. 0876.54016</ref> of a small (cardinality [[Cardinality of the continuum|continuum]]) example.1 KB (162 words) - 06:21, 9 June 2009
- * For mathematical topics see [[Cardinality]] for the concept, and [[Cardinal number]] for the theory292 bytes (34 words) - 17:22, 27 June 2009
- ...This may be explained intuitively by stating that if we simply take as the cardinality of the union the sum of the cardinalities of the constituent sets, then we1 KB (237 words) - 19:41, 7 April 2009
- ==Bijections and the concept of cardinality== ...we say the sets have the same cardinality or the same [[cardinal number]]. Cardinality can be thought of as a generalization of number of elements of finite sets.4 KB (618 words) - 22:24, 7 February 2010
- {{r|cardinality}}172 bytes (23 words) - 18:48, 6 July 2009
- see [[Cardinality/Bibliography]] for more references390 bytes (51 words) - 16:59, 17 June 2009
- {{r|Cardinality}}307 bytes (44 words) - 16:27, 26 July 2008
- {{r|cardinality}}189 bytes (21 words) - 16:20, 17 June 2009
- {{r|cardinality}}182 bytes (22 words) - 18:39, 20 June 2009
- {{r|cardinality}}146 bytes (17 words) - 15:52, 17 June 2009
- '''Cardinality''' is the notion that answers the question "How many?", However, the concept of cardinality can be understood without having names for numbers,2 KB (347 words) - 18:14, 26 June 2009
- {{r|cardinality}} -->206 bytes (26 words) - 16:28, 11 June 2009
- {{r|Cardinality}}267 bytes (32 words) - 19:16, 17 June 2009
- ...l [[cardinality]] is a '''transcendence basis''' for ''E''/''F'', and this cardinality is the '''transcendence degree''' or '''transcendence dimension''' of ''E''2 KB (253 words) - 17:52, 6 January 2009
- {{r|cardinality}} -->149 bytes (18 words) - 18:35, 15 July 2009
- {{r|Cardinality}}477 bytes (65 words) - 07:22, 22 July 2011
- {{r|Cardinality}}515 bytes (67 words) - 16:45, 11 January 2010
- ...ring for which any two bases for a free module over the ring have the same cardinality is said to have the [[invariant dimension property]].2 KB (371 words) - 00:36, 2 February 2009
- The '''order''' of a group is just its [[cardinality]] as a set. The connexion between the two is that the order of an element857 bytes (146 words) - 13:24, 1 February 2009
- ...s. Some of the intuitive notions associated with size do not carry over to cardinality, and some do in certain set theories but not in others. The cardinality of a set ''X'' then, will be an object associated with ''X'', which we deno11 KB (1,808 words) - 17:50, 26 June 2009
- A special case of size is [[cardinality]],1 KB (191 words) - 17:30, 15 July 2009
- i.e., its [[cardinality]] (the number of its elements) is a natural [[number]].1 KB (222 words) - 16:36, 4 January 2013
- == Cardinality ==7 KB (1,145 words) - 00:49, 20 October 2013
- In the context of counting, '''zero''' is the smallest [[cardinality]], the number of elements in the empty set.2 KB (326 words) - 18:28, 17 July 2009
- ...ine the '''rank''' ρ(''A'') of a subset ''A'' of ''E'' to be the maximum [[cardinality]] of an independent subset of ''A''. The rank satisfies the following2 KB (334 words) - 16:29, 7 February 2009
- The ''rank'' of a free group is the [[cardinality]] of a generating set. A subgroup of a free group is again free, but the r2 KB (436 words) - 02:56, 15 November 2008
- ...l number|transcendental]]. The non-existence of a subset of the reals with cardinality strictly between that of the integers and the reals is known as the [[conti ...real numbers themselves. The set of [[hyperreal number]]s <!--is equal in cardinality to '''R''' and also--> satisfies the same first order sentences as '''R'''.19 KB (2,948 words) - 10:07, 28 February 2024
- ...[[one-to-one correspondence]] with its [[power set]]: equivalently, the [[cardinality]] of a set is strictly less than that of its power set. The argument proce4 KB (745 words) - 23:17, 25 October 2013
- ==== Cardinality ==== ...4,6,8, ...}. One is a subset of the other. Nevertheless they have the same cardinality, as is shown by the correspondence mapping ''n'' in the former set to 2''n'22 KB (3,815 words) - 15:46, 23 September 2013
- ==== Cardinality ==== ...4,6,8, ...}. One is a subset of the other. Nevertheless they have the same cardinality, as is shown by the correspondence mapping ''n'' in the former set to 2''n'24 KB (4,193 words) - 15:48, 23 September 2013
- ...ilar" is interpreted as [[Bijective function#Bijections and the concept of cardinality|equinumerous]].6 KB (944 words) - 08:32, 14 October 2013
- ...ilar" is interpreted as [[Bijective function#Bijections and the concept of cardinality|equinumerous]].6 KB (944 words) - 15:09, 23 September 2013
- ...a finite set contains is called that set's [[cardinality]]. The concept of cardinality can also be applied to infinite sets, though the concept is less intuitive, ...lacing bars around the name of the set. For example, one would express the cardinality of the above set as such:17 KB (2,828 words) - 10:37, 24 July 2011
- ...y seem obvious it needs a proof, and it is crucial for the definition of [[cardinality]] to make sense.8 KB (1,281 words) - 15:39, 23 September 2013
- ...y seem obvious it needs a proof, and it is crucial for the definition of [[cardinality]] to make sense.8 KB (1,275 words) - 15:34, 23 September 2013
- ...<strong>2</strong>], the skeletal version of the full category of sets of cardinality < 2<ref>Category <strong>2</strong> was suggested by Fred Linton in the [ht7 KB (1,151 words) - 14:44, 26 December 2013
- In terms of cardinal numbers and their arithmetic the [[cardinality]] of a countably infinite set is [[aleph-0|aleph-null]],10 KB (1,462 words) - 17:24, 25 August 2013
- In terms of cardinal numbers and their arithmetic the [[cardinality]] of a countably infinite set is [[aleph-0|aleph-null]],10 KB (1,462 words) - 17:25, 25 August 2013
- ...s are comparable. The ''width'' of a partially ordered set is the largest cardinality of an antichain.11 KB (1,918 words) - 18:23, 17 January 2010
- Cantor (who introduced sets and [[cardinality|cardinal numbers]]) believed this to be true, but tried in vain to prove it8 KB (1,289 words) - 20:20, 15 July 2009
- the concept of [[cardinality]], 0 is usually included into the natural numbers.16 KB (2,562 words) - 00:45, 13 October 2009
- ...etation: they enumerate [[alternating permutation]]s of finite sets of odd cardinality. ...tation: they enumerate [[alternating permutation]]s of finite sets of even cardinality.33 KB (5,179 words) - 08:26, 4 June 2010
- The ''order'' of a group ''G'', denoted by |''G''| or o(''G''), is the [[cardinality|number of elements]] of the set ''G''. A group is called ''finite'' if it h19 KB (3,074 words) - 11:11, 13 February 2009