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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
• 1995 USAMO Problems/Problem 4
  Since <math>kQ(x)</math> satisfies these relations as well, and <math>kq_m=kQ(m)</math>,
  3 KB (502 words) - 15:27, 11 May 2018
• 1951 AHSME Problems/Problem 27
  <math> \textbf{(E)}\ \text{none of the above relations are true} </math> ...-All of the relationships don't work so we must choose the last choice, no relations.
  2 KB (321 words) - 15:48, 10 September 2018
• 1958 AHSME Problems/Problem 29
  ...h> and <math> \overline{EC}</math> are drawn. Which of the following angle relations is true?
  996 bytes (169 words) - 06:21, 3 October 2014
• 1975 AHSME Problems
  A woman, her brother, her son and her daughter are chess players (all relations by birth). The worst player's twin (who is one of the four players) and the
  16 KB (2,512 words) - 04:48, 27 November 2021
• 2006 iTest Problems
  ...positive reals <math>x</math>, <math>y</math>, <math>z</math> satisfy the relations
  31 KB (4,811 words) - 00:02, 4 November 2023
• MIE 2015/Day 1/Problem 6
  So we got these three relations
  6 KB (962 words) - 00:39, 1 September 2021
• MIE 2015/Day 1/Problem 2
  By Girard's relations (also called Vieta's formulas or Newton's identities),
  650 bytes (110 words) - 14:25, 11 January 2018
• 2018 AIME I Problems/Problem 7
  ...the prism is symmetrical) to all the other 11 vertices. Using Pythagorean relations, we find that the distances are <math>1</math>, <math>\sqrt{3}</math>, <mat
  6 KB (1,023 words) - 10:38, 21 November 2023
• 2019 AMC 12A Problems/Problem 25
  ...</math>, we have <math>x_n=180^\circ-2x_{n-1}</math> (identical recurrence relations can be derived for <math>y_n</math> and <math>z_n</math>). To find an expli
  5 KB (933 words) - 22:23, 2 January 2024
• 2004 IMO Problems
  ...a,b,c</math> such that <math>ab + bc + ca = 0</math> we have the following relations
  3 KB (488 words) - 04:36, 21 February 2021
• 1995 IMO Problems/Problem 4
  ...eal numbers <math>x_0, x_1, x_2,.....x_{1994}, x_{1995}</math> satisfy the relations
  2 KB (389 words) - 03:43, 26 November 2023
• What is the definition of Pure Mathematics?
  ...definition of geometry is ''Geometry is concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs''. Or th
  35 KB (5,882 words) - 18:08, 28 June 2021
• Classical Mechanics
  ...y of (relative) motion - displacement, velocity, acceleration etc. The two relations at the heart of kinematics are:
  3 KB (423 words) - 12:58, 8 July 2019
• 1979 IMO Problems
  ...exists positive reals <math>x_{1}, \ldots, x_{5}</math> which satisfy the relations <math> \sum_{k=1}^{5} kx_{k}=a,</math> <math> \sum_{k=1}^{5} k^{3}x_{k}=a^{
  3 KB (448 words) - 17:10, 29 January 2021
• 1972 AHSME Problems/Problem 25
  ...h>\overline{BD}=x</math> and <math>\angle{DAB}=y</math>. By LoC we get the relations
  1 KB (237 words) - 10:14, 29 January 2021
• 1975 AHSME Problems/Problem 25
  A woman, her brother, her son and her daughter are chess players (all relations by birth). The worst player's twin (who is one of the four players) and the
  2 KB (458 words) - 14:42, 17 August 2021
• 1979 IMO Problems/Problem 5
  ...sts non-negative reals <math>x_{1}, \ldots, x_{5}</math> which satisfy the relations <math> \sum_{k=1}^{5} kx_{k}=a,</math> <math> \sum_{k=1}^{5} k^{3}x_{k}=a^{
  2 KB (391 words) - 10:55, 30 September 2022
• 1991 IMO Problems/Problem 3
  ...s) remove <math> S_{p,q}</math> and so on, and these have similar ordering relations.
  6 KB (911 words) - 17:45, 30 January 2021
• 2021 Fall AMC 12A Problems/Problem 13
  ...> to simplify. By <math>45</math>-<math>45</math>-<math>90</math> triangle relations (or distance formula), <math>AD = 2b\sqrt{2}.</math>
  16 KB (2,526 words) - 00:53, 6 May 2023
• 2022 AMC 12B Problems/Problem 25
  ...\sqrt{2}}{2},</math> and <math>x</math>. By <math>30-60-90</math> triangle relations, the largest altitude of the orange triangle is <math>\frac{x\sqrt{6}}{2}.< ...dot \sqrt{3} =\frac{\sqrt{3}}{2}</math>, by <math>30-60-90</math> triangle relations. The height of the hexagon is twice this value, or <math>\sqrt{3}.</math>
  20 KB (2,980 words) - 18:17, 2 January 2024
• 2023 AMC 12B Problems
  ...> and <math>d</math> are positive integers satisfying all of the following relations.
  13 KB (2,107 words) - 22:19, 20 April 2024
• 2023 AMC 10B Problems/Problem 20
  ...>4</math>, giving us through <math>45^{\circ}-45^{\circ}-90^{\circ}</math> relations and Pythagorean theorem a diameter for each semi-circle of <math>2\sqrt{2}<
  5 KB (829 words) - 11:53, 29 February 2024
• 2023 AMC 12B Problems/Problem 24
  ...> and <math>d</math> are positive integers satisfying all of the following relations.
  3 KB (499 words) - 02:57, 20 November 2023