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- A '''mathematical proof''' is a way to show that a [[mathematics|math]] [[theorem]] is true. One mu == Proof by Induction == ...4 KB (758 words) - 05:51, 9 March 2015
- ...[http://en.wikipedia.org/wiki/VC_dimension '''VC dimension'''] is defined by the power of a family to shatter a set. ...F})</math>, is the size of the largest <math>R\subseteq X</math> shattered by <math>\mathcal{F}</math>. ...25 KB (4,480 words) - 04:58, 17 November 2010
- ...[http://en.wikipedia.org/wiki/VC_dimension '''VC dimension'''] is defined by the power of a family to shatter a set. ...F})</math>, is the size of the largest <math>R\subseteq X</math> shattered by <math>\mathcal{F}</math>. ...25 KB (4,480 words) - 08:23, 16 August 2011
- ...antor|Cantor]] published articles on it in 1877, 1891 and 1899. His first proof of the diagonal argument was published in 1890 in the [[journal]] of the [[ By omitting fractions that can still be simplified, there is a [[Bijective fun ...12 KB (1,234 words) - 02:16, 5 September 2016
- * <math>R(4,3)\leq 9</math>. (Hint: Proof by contradiction. Color the edges of <math>K_9</math> in red and blue, and assume that there ...</math> and that all the vertices of <math>T\subseteq B</math> are matched by <math>M'</math>. Prove that <math>G</math> contains a matching that matches ...2 KB (461 words) - 02:48, 10 June 2023
- === First proof (shadows)=== We first introduce the original proof by Sperner, which uses concepts called '''shadows''' and '''shades''' of set s ...24 KB (4,365 words) - 11:50, 5 June 2013
- === First proof (shadows)=== We first introduce the original proof by Sperner, which uses concepts called '''shadows''' and '''shades''' of set s ...25 KB (4,389 words) - 09:05, 12 January 2011
- {{Proof| We proceed by induction on <math>k</math>. For <math>k=1</math>, <math>\mathcal{F}\subset ...25 KB (4,523 words) - 13:54, 27 December 2015
- === First proof (shadows)=== We first introduce the original proof by Sperner, which uses concepts called '''shadows''' and '''shades''' of set s ...25 KB (4,408 words) - 01:20, 10 November 2011
- {{Proof| We proceed by induction on <math>k</math>. For <math>k=1</math>, <math>\mathcal{F}\subset ...50 KB (8,991 words) - 12:23, 21 May 2023
- {{Proof| We proceed by induction on <math>k</math>. For <math>k=1</math>, <math>\mathcal{F}\subset ...32 KB (5,780 words) - 13:32, 2 December 2017
- {{Proof| We proceed by induction on <math>k</math>. For <math>k=1</math>, <math>\mathcal{F}\subset ...32 KB (5,780 words) - 02:49, 24 November 2016
- {{Proof| We proceed by induction on <math>k</math>. For <math>k=1</math>, <math>\mathcal{F}\subset ...32 KB (5,780 words) - 07:54, 28 November 2019
- === First proof (shadows)=== We first introduce the original proof by Sperner, which uses concepts called '''shadows''' and '''shades''' of set s ...32 KB (5,800 words) - 07:57, 21 May 2014
- ...proof uses the famous Cauchy-Schwarz inequality in analysis. And the third proof uses another famous inequality: the inequality of the arithmetic and geomet {{Prooftitle|First proof. (pigeonhole principle)| ...18 KB (3,527 words) - 06:10, 22 November 2017
- ...proof uses the famous Cauchy-Schwarz inequality in analysis. And the third proof uses another famous inequality: the inequality of the arithmetic and geomet {{Prooftitle|First proof. (pigeonhole principle)| ...18 KB (3,527 words) - 05:10, 9 November 2016
- ...proof uses the famous Cauchy-Schwarz inequality in analysis. And the third proof uses another famous inequality: the inequality of the arithmetic and geomet {{Prooftitle|First proof. (pigeonhole principle)| ...18 KB (3,527 words) - 05:55, 12 November 2019
- ...proof uses the famous Cauchy-Schwarz inequality in analysis. And the third proof uses another famous inequality: the inequality of the arithmetic and geomet {{Prooftitle|First proof. (pigeonhole principle)| ...18 KB (3,527 words) - 08:55, 4 May 2023
- ...proof uses the famous Cauchy-Schwarz inequality in analysis. And the third proof uses another famous inequality: the inequality of the arithmetic and geomet {{Prooftitle|First proof. (pigeonhole principle)| ...19 KB (3,541 words) - 07:47, 25 December 2015
- ...and how to efficiently find a stable matching. Both questions are answered by the following proposal algorithm due to Gale and Shapley. ...hus <math>m'</math> becomes single again and considers himself as rejected by <math>w</math>) and is married to <math>m</math>; ...24 KB (4,172 words) - 15:38, 19 March 2013