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- ...eory]], a '''graph''' is a (usually [[finite]]) [[empty set | nonempty]] [[set]] of [[vertex|vertices]] that are joined by a number (possibly zero) of [[e ...then <math>E</math> may be defined using ordered pairs from the [[product set]] <math>V \times V</math>.8 KB (1,428 words) - 10:26, 27 August 2020
- If <math>A</math> and <math>B</math> are [[partially ordered set]]s, a homomorphism from <math>A</math> to <math>B</math> is a mapping <math2 KB (303 words) - 15:33, 11 February 2024
- ...e number such that <math>ab^2=\log_{10}b</math>, what is the median of the set <math>\{0,1,a,b,1/b\}</math>? This puts <math>a</math> as the smallest in the set since it must be negative.1 KB (242 words) - 03:05, 19 May 2024
- ...glazed, and powdered donuts she wound up with. Find the number of possible ordered triples <math>(a, b, c)</math>. ...ng consecutively as he writes. When he stops, he realizes that there is no set of 5 composite integers among the ones he wrote such that each pair of thos5 KB (769 words) - 20:56, 24 March 2015
- A '''filter''' on a [[set]] <math>X</math> is a structure of [[subset]]s of <math>X</math>. Let <math>\mathcal{F}</math> be a set of subsets of <math>X</math>. We say that <math>\mathcal{F}</math> is a fi2 KB (368 words) - 21:14, 13 October 2019
- An '''ultrafilter''' is a [[set theory | set theoretic]] structure. An ultrafilter on a set <math>X</math> is a non-empty [[filter]] <math>\mathcal{F}</math> on <math>9 KB (1,685 words) - 20:28, 13 October 2019
- ...ure that is as general as possible—a magma generated from an initial set with no constraints or relations. The free magma generated from a [[set]] <math>X</math> is constructed as follows.4 KB (887 words) - 13:19, 6 July 2016
- ...sult in [[group theory]] that is useful for counting the [[orbit]]s of a [[set]] on which a [[group]] [[group action|acts]]. ...<math>\alpha \in G</math>, let <math>\text{fix}(\alpha)</math> denote the set of [[fixed point]]s of <math>\alpha</math>. Then5 KB (757 words) - 18:11, 23 October 2023
- |Devise a set of denominations, as few as possible, such that any integer value from 1 to |For which n can the complete graph K_n have its set of edges partitioned to form edge-disjoint Hamiltonian circuits or Hamitoni22 KB (3,358 words) - 15:17, 18 July 2017
- ...the '''quotient field'''), denoted by <math>\text{Frac}(R)</math>, as the set <math>\left\{\frac{a}{b} \mid a,b\in R, b\neq 0\right\}</math>. This is ana ...math>ad = bc</math>. Then we can define <math>\text{Frac}(R)</math> as the set of [[equivalence class|equivalence classes]] of <math>S</math> under <math>2 KB (439 words) - 14:09, 4 March 2022
- ...hat are the product of two consecutive integers. Let <math>B</math> be the set of positive integers that are the product of three consecutive integers. Fi ...lean up the storage shed. After clearing away some trash, Joshua and Wendy set aside give boxes that belong to the two of them that they decide to take up71 KB (11,749 words) - 01:31, 2 November 2023
- Consider the set of all triangles <math>OPQ</math> where <math>O</math> is the origin and <m *There are 48 ordered pairs <math>(x_2,x_1)</math> such that their positive difference is 2.8 KB (1,319 words) - 15:01, 16 August 2020
- Let <math>S</math> be a [[partially ordered set]]. We say that <math>S</math> satisfies the '''ascending chain condition'' ...th>S</math> satisfies the '''descending chain condition''' ('''DCC'''). A set <math>S</math> with an ordering <math>\leqslant</math> satisfies ACC if and2 KB (314 words) - 18:00, 15 December 2018
- When three different numbers from the set <math>\{ -3, -2, -1, 4, 5 \} </math> are multiplied, the largest possible p ...s of concrete must a contractor order for the sidewalk if concrete must be ordered in a whole number of cubic yards?15 KB (2,059 words) - 15:03, 6 October 2021
- ...g <math>2p+2q+2r = 10</math>. We just need to take the lowest value in the set, square root it, and subtract the resulting value from 5 to get <math>\boxe ...^2+r^2+4pq+4pr+4qr = 29</math> to obtain <cmath>p^2+q^2+r^2=21</cmath> The ordered triple {16,4,1} sums to 21, and the answer choices are all positive integer5 KB (969 words) - 21:33, 22 June 2022
- ...s less than <math>20</math> are there exactly two distinct elements in the set <math>\{i^x, (1+i)^y, z\}</math>, where <math>i=\sqrt{-1}</math>? ...c</math> are randomly and independently selected with replacement from the set <math>\{1, 2, 3,\dots, 2010\}</math>. What is the probability that <math>ab12 KB (1,845 words) - 13:00, 19 February 2020
- ...he number of minimally intersecting ordered triples of sets for which each set is a subset of <math>\{1,2,3,4,5,6,7\}</math>. Find the remainder when <mat '''Note''': <math>|S|</math> represents the number of elements in the set <math>S</math>.8 KB (1,243 words) - 21:58, 10 August 2020
- ...he number of minimally intersecting ordered triples of sets for which each set is a subset of <math>\{1,2,3,4,5,6,7\}</math>. Find the remainder when <mat '''Note''': <math>|S|</math> represents the number of elements in the set <math>S</math>.2 KB (255 words) - 17:03, 9 August 2018
- ...th>S=\{ 1,2,3,4,5\}</math> (where the product of the elements of the empty set is taken to be 1). If we pair each subset <math>P</math> with its complemen .../math> themselves, and let <math>C=\{1,2,3,4,5\} - (A\cup B)</math> be the set of the remaining values. Notice that all possible values of <math>f(f(x))</36 KB (6,214 words) - 20:22, 13 July 2023
- Let <math>N</math> be the number of [[ordered pair]]s of nonempty sets <math>\mathcal{A}</math> and <math>\mathcal{B}</ma Let us [[partition]] the set <math>\{1,2,\cdots,12\}</math> into <math>n</math> numbers in <math>A</math4 KB (699 words) - 20:57, 20 July 2023
