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• 1994 AIME Problems/Problem 15
  ...s cut out <math>120^{\circ}, 60^{\circ}</math> angles by simple similarity relations and angle-chasing.
  4 KB (717 words) - 22:20, 3 June 2021
• 2001 AIME I Problems/Problem 14
  ...maller cases, which is something that we don't like -- we want to keep our relations as simple as possible. Therefore, seeing that we can't work forwards anymor
  13 KB (2,298 words) - 19:46, 9 July 2020
• Equation
  5 KB (932 words) - 12:57, 26 July 2023
• 2006 Romanian NMO Problems
  ...atrix <math>A\in\mathcal M_n(\mathbb C)</math> a matrix which fulfills the relations
  11 KB (1,779 words) - 14:57, 7 May 2012
• Navier-Stokes Equation
  ...ariable]]s of interest (e.g. velocity and pressure), rather they establish relations among the rates of change or fluxes of these quantities. In mathematical te
  3 KB (553 words) - 22:08, 2 May 2022
• Binary relation
  ...icular interest. This more general definition is useful because it admits relations whose "domain" is a class of sets too large to constitute a set. For insta
  4 KB (655 words) - 22:33, 18 May 2008
• Partially ordered set
  ...the poset <math>P</math> has 8 elements among which we have the following relations: :* Among the other 6 elements, we have the relations <math>\{1\} \leq \{1, 2\}</math>, <math>\{1\} \leq \{1, 3\}</math>, <math>\
  4 KB (717 words) - 20:01, 25 April 2009
• Boolean lattice
  ...}</math> is larger than all others, and the other six elements satisfy the relations <math>\{1\}, \{2\} \subset \{1,2\}</math>, <math>\{1\}, \{3\} \subset \{1,3
  1 KB (168 words) - 22:46, 20 April 2008
• 1981 IMO Problems/Problem 5
  ...s on the [[angle bisector | bisector]] of angle <math>A</math> and similar relations hold for the triangles' other corresponding points, the center of homothety
  2 KB (373 words) - 23:09, 29 January 2021
• Predicate
  ...he set-theoretic relations <math>\in</math> and <math>=</math>. Additional relations can be made with predicates by using propositional logic quantifiers such a
  1 KB (228 words) - 18:07, 26 March 2022
• Totally ordered set
  1 KB (174 words) - 12:52, 25 November 2007
• Comparable
  ...b</math> of <math>S</math> are '''comparable''' if and only if one of the relations <math>R(a, b)</math> and <math>R(b, a)</math> holds. Otherwise, the two el
  369 bytes (65 words) - 13:04, 9 February 2007
• Incomparable
  ...ath>a, b</math> of <math>S</math> are '''incomparable''' if neither of the relations <math>R(a, b)</math> and <math>R(b, a)</math> holds. Otherwise, the two el
  361 bytes (62 words) - 13:05, 9 February 2007
• Symmetric property
  The notion of symmetry can be extended to broader contexts than binary relations, as well. For example, one could call a general relation symmetric if the
  1 KB (193 words) - 11:59, 22 May 2007
• 1990 USAMO Problems/Problem 2
  We claim that the following set of relations hold true for all natural numbers <math>n</math> and nonnegative reals <mat
  2 KB (322 words) - 19:14, 18 July 2016
• Relation
  Examples of relations include the relation of [[similarity]] on the set of [[triangle]]s in a [[p ...luding all of those mentioned in the preceding paragraph) are the [[binary relations]], so we begin with them.
  2 KB (445 words) - 08:16, 21 August 2009
• 1951 AHSME Problems
  <math> \textbf{(E)}\ \text{none of the above relations are true} </math>
  23 KB (3,646 words) - 21:53, 21 June 2024
• 2001 USA TST Problems/Problem 8
  ..._1, m_2</math> satisfy <math>m_1m_2 = (n-5)^2</math>. Hence the recursive relations given at the beginning of the problem give all solutions, as desired. We m
  3 KB (448 words) - 21:41, 23 April 2008
• Normal subgroup
  From the characterizations of relations compatible with left and right translation (see the article on [[coset]]s),
  15 KB (2,840 words) - 12:22, 9 April 2019
• Quotient set
  == Compatible relations; derived relations; quotient structure == ...lence classes form a structure of the same species as <math>S</math> under relations derived from passing to quotients, <math>\mathcal{R}</math> is said to be c
  2 KB (358 words) - 09:42, 7 June 2016

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