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• Binary relations
  28 bytes (3 words) - 08:28, 21 August 2009

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• Physics
  ...y of (relative) motion - displacement, velocity, acceleration etc. The two relations at the heart of kinematics are:
  9 KB (1,355 words) - 07:29, 29 September 2021
• Inequality
  ...tary algebra]], and relate slightly to [[number theory]]. They deal with [[relations]] of [[variable]]s denoted by four signs: <math>>,<,\ge,\le</math>.
  12 KB (1,798 words) - 16:20, 14 March 2023
• Recursion
  ...th>n</math>th Fibonacci number, the sequence is defined recursively by the relations <math>F_0 = F_1 = 1</math> and <math>F_{n+1}=F_{n}+F_{n-1}</math>. (That i
  2 KB (316 words) - 16:03, 1 January 2024
• Trigonometry
  '''Trigonometry''' is the study of relations between the side lengths and angles of triangles through the '''trigonometr
  8 KB (1,217 words) - 20:15, 7 September 2023
• Equivalence relation
  Some common examples of equivalence relations:
  1 KB (179 words) - 11:51, 22 May 2007
• Mathematicial notation
  Again, the same relations as above hold.
  8 KB (1,401 words) - 13:11, 17 June 2008
• LaTeX:Symbols
  ==Relations== Negations of many of these relations can be formed by just putting \not before the symbol, or by slipping an "n"
  16 KB (2,324 words) - 16:50, 19 February 2024
• 2002 AMC 12A Problems
  ...} n^2</math>. Let <math>N=f(11)+f(13)+f(14)</math>. Which of the following relations is true?
  12 KB (1,792 words) - 13:06, 19 February 2020
• 2004 AIME I Problems/Problem 15
  Now by using the above relations repeatedly, we find .../math> for <math>n\ge 13</math>. For smaller values, it is easy to use the relations to compute that the terms are powers of <math>2</math>, although we note th
  9 KB (1,491 words) - 01:23, 26 December 2022
• 1985 AIME Problems/Problem 12
  ...ity that the bug is on some other vertex. We have the following recurrence relations. <cmath>A_n = \frac{1}{3}O_{n-1}</cmath> <cmath>O_n = A_{n-1} + \frac{2}{3}
  17 KB (2,837 words) - 13:34, 4 April 2024
• 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 (3,641 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
• 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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