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• Probability
  ...oss. In this case, <math>\Omega = \{H, T\}</math>, <math>\mathfrak{a} = \{\emptyset, \{H\}, \{T\}, \{H, T\}\}</math>, and <math>\mathit{P}</math> assigns the f <math>\mathit{P}(\emptyset)=0</math>,
  4 KB (588 words) - 12:47, 2 October 2022
• Subset
  <math>\emptyset \subset \{1, 2\} \subset \mathbb{N} \subset \mathbb{Z} \subset \mathbb{Q} \
  1 KB (217 words) - 09:32, 13 August 2011
• LaTeX:Symbols
  |<math>\prime</math>||\prime||<math>\emptyset</math>||\emptyset||<math>\nabla</math>||\nabla
  16 KB (2,324 words) - 16:50, 19 February 2024
• Set
  ...nt}S</math>. For example, <math>\bigcap_{S\,is\,P(A)\,for\,some\,set\,A}S=\emptyset</math>, or the empty set defined next. An [[empty set]], denoted <math>\emptyset</math> is a set with no elements.
  11 KB (2,021 words) - 00:00, 17 July 2011
• Empty set
  The '''Empty Set''' (generally denoted <math>\emptyset</math> or <math>\varnothing</math>) is the (unique) [[set]] containing no e
  489 bytes (84 words) - 21:33, 27 February 2020
• 2004 AIME I Problems/Problem 15
  ...not in any of the other sets. Also, we note that <math>\mathcal{A}_{1,k}=\emptyset</math> for <math>k=0,2,3,4,5,6,7,8,9</math>.
  9 KB (1,491 words) - 01:23, 26 December 2022
• 2002 AIME II Problems/Problem 9
  ...math> ways to organize the elements of <math>S</math> such that <math>B = \emptyset</math> and <math>S = A+C</math>. But, the combination such that <math>A = B = \emptyset</math> and <math>S = C</math> is counted twice.
  3 KB (396 words) - 14:19, 19 October 2018
• Power set
  ...set]] has only one subset, itself. Thus <math>\mathcal{P}(\emptyset) = \{\emptyset\}</math>. ...ets, the empty set and the entire set. Thus <math>\mathcal{P}(\{a\}) = \{\emptyset, \{a\}\}</math>.
  4 KB (757 words) - 11:44, 8 March 2018
• Partially ordered set
  :* <math>\emptyset</math> is a minimal element of the poset; every other element is larger.
  4 KB (717 words) - 20:01, 25 April 2009
• Boolean lattice
  ...\{1, 3\}, \{2, 3\}</math> and <math>\{1, 2, 3\}</math>, among which <math>\emptyset</math> is smaller than all others, <math>S = \{1, 2, 3\}</math> is larger t
  1 KB (168 words) - 22:46, 20 April 2008
• 2007 USAMO Problems/Problem 4
  ...ack) be two complementary animals in <math>D</math>, i.e. <math>R\cap B = \emptyset</math> and <math>R\cup B = D</math>. Suppose <math>|R|\leq s - 1</math>. Th
  10 KB (1,878 words) - 14:56, 30 June 2021
• Zermelo-Fraenkel Axioms
  ...tement:''' There exists a set (called the [[empty set]] and denoted <math>\emptyset</math>) which contains no elements.
  4 KB (732 words) - 20:49, 13 October 2019
• Graph (graph theory)
  ...G = (V, E_1 \cup E_2)</math> is a complete graph and <math>E_1 \cap E_2 = \emptyset</math> then <math>G_2</math> is said to be the ''complement'' of <math>G_1<
  8 KB (1,428 words) - 10:26, 27 August 2020
• Filter
  * <math>F\neq\emptyset</math>.
  2 KB (368 words) - 21:14, 13 October 2019
• 2001 USAMO Problems/Problem 5
  Since <math>S\neq \emptyset</math> by (A), it suffices to prove that <math>m = 1</math>. For the sake o
  3 KB (599 words) - 07:44, 23 October 2022
• 2009 USAMO Problems/Problem 2
  .../math> for all <math>a,b,c\in S</math> implies that <math>-S\cap(S_++S_-)=\emptyset</math>. Since any element of <math>S_++S_-</math> has absolute value at mos
  8 KB (1,444 words) - 03:44, 2 October 2015
• 2010 AIME I Problems
  ...\cap B| = |B \cap C| = |C \cap A| = 1</math> and <math>A \cap B \cap C = \emptyset</math>. For example, <math>(\{1,2\},\{2,3\},\{1,3,4\})</math> is a minimall ...a pair of sets <math>A</math>, <math>B</math> such that <math>A \cap B = \emptyset</math>, <math>A \cup B = S</math>.
  8 KB (1,243 words) - 21:58, 10 August 2020
• 2010 AIME I Problems/Problem 7
  ...\cap B| = |B \cap C| = |C \cap A| = 1</math> and <math>A \cap B \cap C = \emptyset</math>. For example, <math>(\{1,2\},\{2,3\},\{1,3,4\})</math> is a minimall
  2 KB (255 words) - 17:03, 9 August 2018
• 2010 AIME I Problems/Problem 12
  ...a pair of sets <math>A</math>, <math>B</math> such that <math>A \cap B = \emptyset</math>, <math>A \cup B = S</math>.
  2 KB (284 words) - 21:56, 25 November 2023
• 2010 AIME II Problems
  <LI> <math>\mathcal{A} \cap \mathcal{B} = \emptyset</math>, </LI>
  8 KB (1,246 words) - 21:58, 10 August 2020

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