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- ...tant in [[set theory]] when dealing with arguments concerning [[infinite]] sets.2 KB (289 words) - 16:17, 13 February 2009
- ...tant in [[set theory]] when dealing with arguments concerning [[infinite]] sets or in permutation and probability.1,016 bytes (141 words) - 02:39, 29 November 2021
- '''Cardinality''' is a property of [[set]]s. For [[finite]] sets, the cardinality of is the number of [[element]]s in that set, i.e. the siz ==Infinite==2 KB (263 words) - 23:54, 16 November 2019
- ...e integer, and let <math> \displaystyle F </math> be an infinite family of sets, each of size <math> \displaystyle r </math>, no two of which are disjoint. ...math> such that <math> A \cup \{x\} </math> is a subset of infinitely many sets in <math> \displaystyle F </math>.4 KB (681 words) - 19:10, 19 April 2007
- ...divided between those which are [[finite]] and those which are countably [[infinite]]. The name "countable" arises because the countably infinite sets are exactly those which can be put into [[bijection]] with the [[natural nu773 bytes (126 words) - 20:35, 26 September 2008
- One can also consider permutations of [[infinite]] sets. In this case, a permutation of a set <math>S</math> is simply a [[bijecti3 KB (422 words) - 10:01, 25 December 2020
- ...every set that is ''not'' uncountable is either [[finite]] or [[countably infinite]]. The most common example of an uncountable set is the set of [[real numb An alternative proof uses [[Cantor's Theorem]], which says that for all sets <math>S</math>, we have <math>|S|<|\mathcal{P}(S)|</math>, where <math>\mat2 KB (403 words) - 19:53, 13 October 2019
- ...we shall present just a brief discussion of the most common properties of sets and operations related to them. ...he set, in which case it is called a finite set. Otherwise we call it an [[infinite]] set. The objects in a set are called the [[element]]s of the set. A commo11 KB (2,019 words) - 16:20, 7 July 2024
- ...6 cards that can be drawn from the deck is 6 times the number of possible sets of 3 cards that can be drawn. Find <math> n. </math> An infinite geometric series has sum 2005. A new series, obtained by squaring each term7 KB (1,119 words) - 20:12, 28 February 2020
- ...cally) be named, one by one, in a finite amount of time is finite. Finite sets include the [[empty set]], which has zero elements, and every set with a [[ * [[Infinite]]532 bytes (92 words) - 09:11, 7 July 2006
- ...isjoint subsets of <math>\mathcal{S}</math>. (Disjoint sets are defined as sets that have no common elements.) Find the remainder obtained when <math>n</ma Two distinct, real, infinite geometric series each have a sum of <math>1</math> and have the same second7 KB (1,177 words) - 14:42, 11 August 2023
- ...d therefore also constitute examples of [[field]]s. All these rings are [[infinite]], as well. Among the finite commutative rings are sets of integers mod <math>m</math> (<math>\mathbb{Z}/m\mathbb{Z}</math>), for a6 KB (994 words) - 05:16, 8 April 2015
- ...The analogous result is also true for [[infinite]] sets (and thus for all sets): for any set <math>S</math>, the cardinality <math>|\mathcal P (S)|</math> ==Size for Finite Sets==4 KB (757 words) - 10:44, 8 March 2018
- ...ordered set]] such as the reals has a maximum. However, many [[infinite]] sets do not. The [[integer]]s, <math>\mathbb Z</math> have no maximum, since fo1 KB (232 words) - 11:55, 9 February 2007
- ...]]. Polyhedra are 3-D analogues of [[polygon]]s. They can be thought of as sets of [[ordered]] triples. ...exist. (In addition, a [[sphere]] could be thought of a polyhedron with an infinite number of faces.)1 KB (193 words) - 22:15, 6 December 2016
- ...<math>n</math> are integers. Is it possible to cover all grid points by an infinite family of discs with non-overlapping interiors if each disc in the family h ...wo classes. Prove that there are at least <math>n</math> pairwise disjoint sets in the same class.3 KB (539 words) - 12:42, 4 July 2013
- ...ll's Paradox]], some restrictions must be put on which collections to call sets. This axiom establishes the most basic property of sets - a set is completely characterized by its elements alone. <br/>4 KB (732 words) - 19:49, 13 October 2019
- ...ing cart with items. But unlike a club that might have vague requirements, sets are defined precisely by their elements. * **Equality:** Two sets are considered equal only if they have exactly the same elements.2 KB (331 words) - 10:44, 28 September 2024
- <math> \textbf{(A) \ } \text{Infinite} \qquad\textbf{(B) \ } 5\frac{1}{4}a \qquad \textbf{(C) \ } 2a \qquad\textb The limit of the sum of an infinite number of terms in a geometric progression is <math> \frac {a}{1- r}</math>23 KB (3,646 words) - 20:53, 21 June 2024
- ...at in general this theorem is not true on infinite sets without permitting infinite compositions of functions.10 KB (1,668 words) - 14:33, 25 May 2008