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- ...element]]s in the [[union]] of a given group of [[set]]s, the size of each set, and the size of all possible [[intersection]]s among the sets. === Two Set Example ===9 KB (1,703 words) - 00:20, 7 December 2024
- ...d <math>B=\{b_1,b_2,\cdots,b_n\}</math> is a permutation of another finite set of real numbers, the quantity <math>a_1b_1+a_2b_2+\cdots+a_nb_n</math> is m Now for the general case. Again, without loss of generality, set <math>a_1 \leq a_2 \leq \cdots \leq a_n</math> and <math>b_1 \leq b_2 \leq5 KB (804 words) - 12:54, 26 January 2023
- The set of real numbers, denoted by <math>\mathbb{R}</math>, is a subset of [[compl ==The set <math>\mathbb{R}~</math>==3 KB (496 words) - 22:22, 5 January 2022
- ...total possibilities of each step and assembles these to enumerate the full set. ...this problem, there are sometimes multiple independent ways to construct a set. In others, however, an alternative method is not apparent, as with the nex12 KB (1,898 words) - 07:42, 19 August 2024
- ...t of values to another set of values, assigning to each value in the first set exactly one value in the second. For instance, one function may map 1 to 1 Let <math>A</math>,<math>B</math> be [[set]]s and let <math>f</math> be a [[subset]] of <math>A\times B</math>, which10 KB (1,761 words) - 02:16, 12 May 2023
- A '''partition''' <math>\mathcal{P}</math> is defined as the ordered <math>n</math>-[[tuple]] of real numbers <math>\mathcal{P}=(x_0,x_1,\ldots, ...agged partition''' <math>\mathcal{\dot{P}}</math> is defined as the set of ordered pairs <math>\mathcal{\dot{P}}=\{([x_{i-1},x_i],t_i)\}_{i=1}^n</math>.1 KB (178 words) - 19:34, 6 March 2022
- Past sets may be ordered from the US Math Kangaroo website. The Canadian and International (primari ...o does not have precalculus concepts (logs, complex numbers, trigonometry, set notation, or summation/product notation) whereas AMC 12 does.6 KB (949 words) - 21:33, 17 November 2024
- ...1, \{2, 3\}, \{1, 2, 3\}\}</math> is 3, and the cardinality of the [[empty set]] is 0. The cardinality of a set <math>A</math> is denoted by <math>|A|</math>. In the above example, the c2 KB (263 words) - 23:54, 16 November 2019
- In their most general form, polygons are an ordered [[set]] of [[vertex|vertices]], <math>\{A_1, A_2, \ldots, A_n\}</math>, <math>n \2 KB (372 words) - 18:04, 30 May 2015
- ...thin angle brackets or parentheses, <math>(x\,\,y\,\,z\,\,...)</math>. The set of vectors over a [[field]] is called a [[vector space]].11 KB (1,876 words) - 18:01, 29 August 2024
- ...<math>n</math>, where <math>n</math> is a positive integer. For how many ordered 4-tuples <math>(k_1, k_2, k_3, k_4)</math> of nonnegative integers can we ...math>C_i</math>, subtract <math>1</math> from each of the cuts to obtain a set of cuts that is counted in <math>C_{i-1}</math>. For example, if <math>\{27 KB (1,276 words) - 19:51, 6 January 2024
- ...these sets (denoted <math>\mathcal{X}\times \mathcal{Y}</math>) gives all ordered pairs <math>(x,y)</math> with <math>x \in \mathcal{X}</math> and <math>y \i ...ial time of relation where for every <math>y \in \mathcal{Y}</math> in the ordered pair <math>(x,y)</math>, there exists a unique <math>x \in \mathcal{X}</mat4 KB (743 words) - 23:28, 17 November 2024
- ...red set is a [[totally ordered set]] <math>(S,\prec)</math> for which each set <math>A\subseteq S</math> has a [[minimum]] element. [[Category:Set theory]]381 bytes (59 words) - 11:40, 2 June 2019
- ...re <math>r!</math> (the [[factorial]] of <math>r</math>) permutations of a set with <math>r</math> distinct objects. ...sider permutations of [[infinite]] sets. In this case, a permutation of a set <math>S</math> is simply a [[bijection]] between <math>S</math> and itself.3 KB (422 words) - 10:01, 25 December 2020
- Let set <math> \mathcal{A} </math> be a 90-element subset of <math> \{1,2,3,\ldots, Let <math> \mathcal{S} </math> be the set of real numbers that can be represented as repeating decimals of the form <7 KB (1,173 words) - 02:31, 4 January 2023
- How many ordered triples of [[integer]]s <math>(a,b,c)</math>, with <math>a \ge 2</math>, <m ...nct numbers <math>a</math> and <math>b</math> are chosen randomly from the set <math>\{ 2, 2^2, 2^3, \ldots, 2^{25} \}</math>. What is the probability tha13 KB (1,965 words) - 21:18, 7 September 2024
- For how many ordered pairs of positive integers <math>(x,y)</math> is <math>x+2y=100</math>? Let <math>S</math> be the set of points <math>(a,b)</math> in the coordinate plane, where each of <math>a13 KB (1,953 words) - 23:31, 25 January 2023
- ...th>\{1, 2, 3, 4, 5\}</math>, and Sergio randomly selects a number from the set <math>\{1, 2, \ldots, 10\}</math>. What is the probability that Sergio's nu ...nine nonzero digits exactly once. What is the smallest possible sum such a set of primes could have?12 KB (1,792 words) - 12:06, 19 February 2020
- ...<math>a,b,c,d,e,f,g</math> and <math>h</math> be distinct elements in the set Let <math>S</math> be the set of ordered triples <math>(x,y,z)</math> of real numbers for which12 KB (1,781 words) - 13:59, 19 July 2024
- How many non-[[empty set | empty]] [[subset]]s <math>S</math> of <math>\{1,2,3,\ldots ,15\}</math> h ...to choose <math>k</math> elements from an ordered <math>n</math> element [[set]] without choosing two consecutive members?9 KB (1,409 words) - 02:59, 8 December 2024