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  • ...describe a linear [[transformation]] between a stationary reference frame and a reference frame in [[constant velocity]]. The equations are given by [[Category:Functions and mappings]] ...
    521 bytes (75 words) - 17:34, 20 October 2015
  • ...ample of a multifunction: the input 3 is associated with both the output b and the output c.]] ...ample: <math>\sqrt{4}</math> could be 2 or -2 because <math>2^2 = 4</math> and <math>(-2)^2 = 4</math>. ...
    881 bytes (123 words) - 22:40, 23 March 2016
  • ...average of the function at those points. Also, a function is convex [[if and only if]] its [[epigraph (mathematics)|epigraph]] is a [[convex set]]. [[Category:Functions and mappings]] ...
    776 bytes (119 words) - 18:26, 12 March 2013
  • ...ing language]]s and other programming languages with support for anonymous functions (those which support [[Closure_(computer_science)#Closures_and_first-class_ ...to write boost lambda is to include <boost/lambda/lambda.hpp> header file, and using namespace boost::lambda, i.e. ...
    3 KB (355 words) - 05:21, 24 November 2013
  • ...87964126 | year=1987| page=51}}</ref><ref>{{cite book|title=Linear Algebra and Its Applications, 2nd ed.|last1=Lax|first1=Peter|publisher=Wiley|isbn=978-0 ...e a ''linear mapping'' if for any two vectors '''x''' and '''y''' in ''V'' and any scalar α in ''K'', the following two conditions are satisfied: ...
    2 KB (254 words) - 00:04, 2 January 2015
  • ...Y) to represent the three parts of the function, the domain, the codomain and the pairing process. ...ary that the pairing is given by an equation. The main idea is that inputs and outputs are paired up somehow even if the process is very complicated or no ...
    4 KB (751 words) - 09:24, 21 January 2017
  • ...metimes called the Newton–Raphson method, named after Sir [[Isaac Newton]] and Joseph Raphson. Here x<sub>n</sub> is the initial guess and x<sub>n+1</sub> is the next guess. The function f (whose zero is being solv ...
    2 KB (292 words) - 02:49, 23 August 2015
  • ...'' shows the value of ζ(''s''): strong colors are for values close to zero and [[hue]] encodes the value's [[complex number|argument]]. ...s the pole of the zeta function; the black spots on the negative real axis and on the critical line Re(''s'') = 1/2 are its zeros.]] ...
    3 KB (534 words) - 10:42, 20 June 2017
  • Let <math>A</math> and <math>B</math> be two finite sets. The cardinality of their union is For three sets <math>A</math>, <math>B</math>, and <math>C</math>, the cardinality of the union of these three sets is compute ...
    33 KB (6,205 words) - 01:11, 22 September 2011
  • ...that ''f''(''a'')=''b''. This means that the [[range (mathematics)|range]] and codomain of ''f'' are the same set.<ref>{{cite web|url=http://mathworld.wo ...dvanced mathematics. The French prefix ''sur'' means ''above'' or ''onto'' and was chosen since a surjective function maps its domain '''on to''' its codo ...
    10 KB (1,438 words) - 06:38, 8 October 2016
  • Let <math>A</math> and <math>B</math> be two finite sets. The cardinality of their union is For three sets <math>A</math>, <math>B</math>, and <math>C</math>, the cardinality of the union of these three sets is compute ...
    33 KB (6,227 words) - 11:45, 15 October 2017
  • Let <math>A</math> and <math>B</math> be two finite sets. The cardinality of their union is For three sets <math>A</math>, <math>B</math>, and <math>C</math>, the cardinality of the union of these three sets is compute ...
    33 KB (6,227 words) - 12:45, 16 March 2023
  • Let <math>A</math> and <math>B</math> be two finite sets. The cardinality of their union is For three sets <math>A</math>, <math>B</math>, and <math>C</math>, the cardinality of the union of these three sets is compute ...
    33 KB (6,227 words) - 07:00, 29 September 2016
  • Let <math>A</math> and <math>B</math> be two finite sets. The cardinality of their union is For three sets <math>A</math>, <math>B</math>, and <math>C</math>, the cardinality of the union of these three sets is compute ...
    33 KB (6,227 words) - 09:51, 19 March 2024
  • Let <math>A</math> and <math>B</math> be two finite sets. The cardinality of their union is For three sets <math>A</math>, <math>B</math>, and <math>C</math>, the cardinality of the union of these three sets is compute ...
    33 KB (6,227 words) - 06:15, 30 September 2019
  • ...mathbf Z/p^n \mathbf Z </math>, where ''p'' is the fixed [[prime number]] and <math> n = 1,2, \dots </math>. We can express this by [[Pontryagin duality] Let <math>\zeta</math> be a primitive <math> p</math>-th root of unity and look at the following tower of number fields: ...
    5 KB (835 words) - 22:27, 8 March 2013
  • ...nbsp;:&nbsp;''A'' → ''B'' that is both an [[injective function|injection]] and a [[surjective function|surjection]]. This means: for every element ''b'' i ...r=2010 |language=English|accessdate=February 2014}}</ref> In the 1930s, he and a group of other mathematicians published a series of books on modern advan ...
    11 KB (1,621 words) - 07:51, 17 July 2016
  • *The function ''y''=''c'' has 2 [[variable| variables]] ''x'' and ''у'' and 1 [[constant]] ''c''. (In this form of the function, we do not see ''x'', b ...'B'' is a constant function if ''f''(''a'') = ''f''(''b'') for every ''a'' and ''b'' in ''A''.<ref>{{cite web|url=http://planetmath.org/ConstantFunction.h ...
    7 KB (1,037 words) - 22:13, 9 August 2014
  • ...''. It is slanted so ''m''&ne;0. See examples with actual values for ''m'' and ''b'' below.)]] ...df|title=The Calculus of Functions of Several Variables, Linear and Affine Functions|last1=Sloughter|first1=Dan|year=2001|language=English|accessdate=February 2 ...
    14 KB (2,194 words) - 00:02, 2 January 2015
  • ...r=2010 |language=English|accessdate=February 2014}}</ref> In the 1930s, he and a group of other mathematicians published a series of books on modern advan ...owever, a '''1-1 correspondence''' is a bijective function (both injective and surjective). This is confusing, so be careful.<ref>{{cite web|url=http://ma ...
    9 KB (1,271 words) - 06:37, 8 October 2016
  • Usually <math>\epsilon</math> is called '''approximation error''' and <math>\delta</math> is called '''confidence error'''. ...uced by [https://en.wikipedia.org/wiki/Flajolet–Martin_algorithm Flajolet and Martin] in 1984. The algorithm can be implemented in [https://en.wikipedia. ...
    25 KB (4,512 words) - 09:09, 20 September 2018
  • Usually <math>\epsilon</math> is called '''approximation error''' and <math>\delta</math> is called '''confidence error'''. ...uced by [https://en.wikipedia.org/wiki/Flajolet–Martin_algorithm Flajolet and Martin] in 1984. The algorithm can be implemented in [https://en.wikipedia. ...
    25 KB (4,512 words) - 05:52, 16 September 2019
  • Usually <math>\epsilon</math> is called '''approximation error''' and <math>\delta</math> is called '''confidence error'''. ...uced by [https://en.wikipedia.org/wiki/Flajolet–Martin_algorithm Flajolet and Martin] in 1984. The algorithm can be implemented in [https://en.wikipedia. ...
    25 KB (4,512 words) - 07:51, 29 September 2020
  • Usually <math>\epsilon</math> is called '''approximation error''' and <math>\delta</math> is called '''confidence error'''. ...uced by [https://en.wikipedia.org/wiki/Flajolet–Martin_algorithm Flajolet and Martin] in 1984. The algorithm can be implemented in [https://en.wikipedia. ...
    25 KB (4,512 words) - 06:13, 9 September 2021
  • Usually <math>\epsilon</math> is called '''approximation error''' and <math>\delta</math> is called '''confidence error'''. ...uced by [https://en.wikipedia.org/wiki/Flajolet–Martin_algorithm Flajolet and Martin] in 1984. The algorithm can be implemented in [https://en.wikipedia. ...
    25 KB (4,512 words) - 15:48, 3 October 2022
  • == Sauer's lemma and VC-dimension == === Shattering and the VC-dimension === ...
    25 KB (4,480 words) - 04:58, 17 November 2010
  • == Sauer's lemma and VC-dimension == === Shattering and the VC-dimension === ...
    25 KB (4,480 words) - 08:23, 16 August 2011
  • *'''The sum rule''': for any '''''disjoint''''' finite sets <math>S</math> and <math>T</math>, the cardinality of the union <math>|S\cup T|=|S|+|T|</math> *'''The product rule''': for any finite sets <math>S</math> and <math>T</math>, the cardinality of the Cartesian product <math>|S\times T|= ...
    39 KB (6,924 words) - 04:31, 17 February 2014
  • *'''The sum rule''': for any '''''disjoint''''' finite sets <math>S</math> and <math>T</math>, the cardinality of the union <math>|S\cup T|=|S|+|T|</math> *'''The product rule''': for any finite sets <math>S</math> and <math>T</math>, the cardinality of the Cartesian product <math>|S\times T|= ...
    39 KB (6,924 words) - 06:09, 31 August 2015
  • *'''The sum rule''': for any '''''disjoint''''' finite sets <math>S</math> and <math>T</math>, the cardinality of the union <math>|S\cup T|=|S|+|T|</math> *'''The product rule''': for any finite sets <math>S</math> and <math>T</math>, the cardinality of the Cartesian product <math>|S\times T|= ...
    39 KB (6,924 words) - 05:21, 16 September 2019
  • *'''The sum rule''': for any '''''disjoint''''' finite sets <math>S</math> and <math>T</math>, the cardinality of the union <math>|S\cup T|=|S|+|T|</math> *'''The product rule''': for any finite sets <math>S</math> and <math>T</math>, the cardinality of the Cartesian product <math>|S\times T|= ...
    39 KB (6,924 words) - 10:39, 27 February 2024
  • *'''The sum rule''': for any '''''disjoint''''' finite sets <math>S</math> and <math>T</math>, the cardinality of the union <math>|S\cup T|=|S|+|T|</math> *'''The product rule''': for any finite sets <math>S</math> and <math>T</math>, the cardinality of the Cartesian product <math>|S\times T|= ...
    39 KB (6,924 words) - 11:03, 6 March 2013
  • *'''The sum rule''': for any '''''disjoint''''' finite sets <math>S</math> and <math>T</math>, the cardinality of the union <math>|S\cup T|=|S|+|T|</math> *'''The product rule''': for any finite sets <math>S</math> and <math>T</math>, the cardinality of the Cartesian product <math>|S\times T|= ...
    39 KB (6,924 words) - 13:22, 16 February 2023
  • *'''The sum rule''': for any '''''disjoint''''' finite sets <math>S</math> and <math>T</math>, the cardinality of the union <math>|S\cup T|=|S|+|T|</math> *'''The product rule''': for any finite sets <math>S</math> and <math>T</math>, the cardinality of the Cartesian product <math>|S\times T|= ...
    39 KB (6,926 words) - 13:07, 1 September 2011
  • *'''The sum rule''': for any '''''disjoint''''' finite sets <math>S</math> and <math>T</math>, the cardinality of the union <math>|S\cup T|=|S|+|T|</math> *'''The product rule''': for any finite sets <math>S</math> and <math>T</math>, the cardinality of the Cartesian product <math>|S\times T|= ...
    39 KB (6,926 words) - 09:09, 30 December 2016
  • *'''The sum rule''': for any '''''disjoint''''' finite sets <math>S</math> and <math>T</math>, the cardinality of the union <math>|S\cup T|=|S|+|T|</math> *'''The product rule''': for any finite sets <math>S</math> and <math>T</math>, the cardinality of the Cartesian product <math>|S\times T|= ...
    39 KB (6,926 words) - 07:43, 1 August 2017
  • ...to[n]</math>. Needless to say, random mapping is an important random model and may have many applications in Computer Science, e.g. hashing. ...in the class. Assume that for each student, his/her birthday is uniformly and independently distributed over the 365 days in a years. We wonder what the ...
    48 KB (8,716 words) - 08:15, 15 October 2023
  • ...do, called the sunflower lemma, is a famous result in extremal set theory, and has some important applications in Boolean circuit complexity. ...<math>|\mathcal{F}|>r-1</math>, we can choose <math>r</math> of these sets and form a sunflower. ...
    32 KB (5,780 words) - 13:32, 2 December 2017
  • ...do, called the sunflower lemma, is a famous result in extremal set theory, and has some important applications in Boolean circuit complexity. ...<math>|\mathcal{F}|>r-1</math>, we can choose <math>r</math> of these sets and form a sunflower. ...
    32 KB (5,780 words) - 02:49, 24 November 2016
  • ...do, called the sunflower lemma, is a famous result in extremal set theory, and has some important applications in Boolean circuit complexity. ...<math>|\mathcal{F}|>r-1</math>, we can choose <math>r</math> of these sets and form a sunflower. ...
    32 KB (5,780 words) - 07:54, 28 November 2019
  • ...ce the original proof by Sperner, which uses concepts called '''shadows''' and '''shades''' of set systems. :Let <math>|X|=n\,</math> and <math>\mathcal{F}\subseteq {X\choose k}</math>, <math>k<n\,</math>. ...
    32 KB (5,800 words) - 07:57, 21 May 2014
  • ...do, called the sunflower lemma, is a famous result in extremal set theory, and has some important applications in Boolean circuit complexity. ...<math>|\mathcal{F}|>r-1</math>, we can choose <math>r</math> of these sets and form a sunflower. ...
    50 KB (8,991 words) - 12:23, 21 May 2023