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• 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
• 2004 IMO Problems/Problem 2
  ...a,b,c</math> such that <math>ab + bc + ca = 0</math> we have the following relations
  2 KB (373 words) - 00:52, 19 November 2023
• 2002 AMC 12A Problems/Problem 14
  ...} n^2</math>. Let <math>N=f(11)+f(13)+f(14)</math>. Which of the following relations is true?
  694 bytes (106 words) - 20:43, 25 August 2022
• 2010 USAMO Problems/Problem 3
  recurrence relations:
  11 KB (1,889 words) - 13:45, 4 July 2013
• 1958 AHSME Problems
  ...h> and <math> \overline{EC}</math> are drawn. Which of the following angle relations is true?
  25 KB (3,872 words) - 14:21, 20 February 2020
• 1998 IMO Shortlist Problems/N1
  We have the following divisibility relations, <cmath>ab^2+b+7|a^2b+a+b|b(a^2b+a+b)=a^2b^2+ab+b^2</cmath>
  947 bytes (169 words) - 04:20, 16 August 2011
• Mock AIME I 2012 Problems/Problem 4
  It is easy to see that we have the following recursive relations: <math>a_n = 3a_{n-1}^2, b_n = 3b_{n-1}^2+2b_{n-1}+1</math>.
  1 KB (250 words) - 17:33, 7 April 2012
• 1988 USAMO Problems/Problem 5
  which gets us the same relations (for <math>n\leq 32</math>).
  8 KB (1,348 words) - 09:44, 25 June 2022
• 1977 USAMO Problems/Problem 3
  First, Vieta's relations give <math>a+b+c+d = -1 , ab+ac+ad+bc+bd+cd=0, abc+abd+acd+bcd=0, abcd = -1
  1 KB (212 words) - 22:46, 20 September 2022
• 2013 USAMO Problems/Problem 2
  For the sake of convenience in determining recurrence relations, we define another type of board with two <math>1\times n</math> boards whe We can determine reccurence relations for <math>s_n</math>, <math>t_n</math>, and <math>u_n</math> in terms of ea
  14 KB (2,076 words) - 20:29, 10 July 2023
• 2013 USAJMO Problems/Problem 1
  ...5a+3 \equiv 3 \pmod 9</math>. So 6 mod 9 case is eliminated from the above relations of congruences
  9 KB (1,494 words) - 02:45, 10 May 2024

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