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• 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 (3,641 words) - 22:23, 3 November 2023
• 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
• Coset
  '''Proposition.''' The relations <math>x^{-1}y \in H</math>, <math>xy^{-1} \in H</math> are [[equivalence re == Cosets and compatible relations ==
  4 KB (897 words) - 01:28, 3 September 2008
• Free magma
  ...ossible&mdash;a magma generated from an initial set with no constraints or relations. == Relations on a free magma; Universal property ==
  4 KB (887 words) - 13:19, 6 July 2016
• Commutator (group)
  == Relations with Commutators == '''Proposition 1.''' For all <math>x,y,z</math> in a group, the following relations hold:
  6 KB (1,325 words) - 00:55, 2 June 2008
• Direct product
  ...he [[Cartesian product]] of the sets <math>A_i</math>, with coordinatewise relations.
  2 KB (280 words) - 12:32, 6 June 2008
• Dynamical Systems
  ...ations]] (ordinary or partial), [[difference equations]], and [[recurrence relations]]. Almost every technical field requires the consideration of dynamical sys
  789 bytes (107 words) - 21:52, 18 October 2017
• Topological space
  ...[[subset]] of the [[power set]] of <math>X</math> satisfying the following relations:
  6 KB (1,142 words) - 15:38, 21 June 2008
• Mechanics
  ...y of (relative) motion - displacement, velocity, acceleration etc. The two relations at the heart of kinematics are: and where is displacement at time , is
  2 KB (309 words) - 15:41, 1 December 2015
• Quotient ring
  == Characterization of Equivalence Relations Compatible with Ring Structure ==
  3 KB (547 words) - 14:13, 16 June 2008
• 2001 IMO Shortlist Problems/G1
  ...triangle A_1EF\sim \triangle A_2BC</math>. The ratio of similarity of both relations is <math>\frac{EF}{BC}</math>, which implies that quadrilaterals <math>AEA_
  3 KB (584 words) - 15:07, 12 December 2011
• Carnot's Theorem
  ...of pythogorean theorem to triangles <math>PXB,PXC</math>. Now with similar relations for <math>Y</math> and <math>Z</math>, Carnot's theorem finishes the job!
  4 KB (723 words) - 01:45, 18 February 2021

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