Create the page "Infinite sets" on this wiki! See also the search results found.

• Topological space
  ...plements are elements of <math>\mathcal{T}</math> are then called ''closed sets''. ...of closed sets is closed, and that the intersection of any family of open sets is open.
  6 KB (1,142 words) - 15:38, 21 June 2008
• 2008 iTest Problems
  ...ploring other quantities associated with the roots of such a quadratic. He sets out to compute the greatest possible value of <math>\dfrac1{r_1^{2008}}+\df ...umber less than <math>2008</math> that is a divisor of some integer in the infinite
  71 KB (11,749 words) - 01:31, 2 November 2023
• Georg Cantor
  ...et of rationals. He first introduced the idea of [[cardinality of infinite sets]] using the symbol <math>\aleph</math> to represent the size. Because his w
  652 bytes (103 words) - 21:32, 13 August 2015
• Tower law
  Furthermore, if either <math>[L:K]</math> or <math>[K:F]</math> is infinite then so is <math>[L:F]</math>. ...ndent sets in <math>L</math> over <math>F</math>, so <math>[L:F]</math> is infinite as well.
  3 KB (567 words) - 08:42, 21 August 2009
• Separation axioms
  ...<math>x,y</math> in a topological space <math>X</math>, there exists open sets <math>U, V</math> such that <math>x \in U, y \in V</math> and <math>U,V</ma ...ath> but not <math>T_2</math> is the [[finite complement topology]] on any infinite space.
  5 KB (672 words) - 13:28, 4 June 2018
• 1967 AHSME Problems
  \textbf{(D)}\ \text{must be infinite}\qquad \textbf{(E)}\ \text{must be zero or infinite}</math>
  20 KB (3,108 words) - 14:14, 20 February 2020
• 2012 USAMO Problems
  ...e which integers <math>n > 1</math> have the property that there exists an infinite sequence <math>a_1</math>, <math>a_2</math>, <math>a_3</math>, <math>\dots< Prove that for any positive number <math>\lambda</math>, the number of sets <math>A</math> satisfying <math>S_A \ge \lambda</math> is at most <math>2^{
  3 KB (507 words) - 03:37, 7 June 2020
• 1962 AHSME Problems
  Which of the following sets of <math>x</math>-values satisfy the inequality <math>2x^2 + x < 6</math>? The limiting sum of the infinite series, <math>\frac{1}{10} + \frac{2}{10^2} + \frac{3}{10^3} + \dots</math>
  17 KB (2,459 words) - 22:40, 10 April 2023
• 2014 USAJMO Problems/Problem 5
  ...e integer. Two players <math>A</math> and <math>B</math> play a game on an infinite grid of regular hexagons. Initially all the grid cells are empty. Then the ...A</math> cannot play under these circumstances. If we look at the disjoint sets
  4 KB (665 words) - 20:18, 18 April 2016
• Searching the community
  ...posts containing the words "interface", "[[incircle]]", "intermediate", "[[infinite]]", etc. will all match the query "in*e". | Sets the default size of a "unit" to a specified value. Default is very small. N
  21 KB (3,334 words) - 23:53, 23 March 2022
• 2016 AMC 10B Problems
  ...ns as sets of triplets. How many of these <math>1000</math> babies were in sets of quadruplets? The sum of an infinite geometric series is a positive number <math>S</math>, and the second term i
  12 KB (1,868 words) - 17:50, 30 December 2023
• 2016 AMC 12B Problems
  The sum of an infinite geometric series is a positive number <math>S</math>, and the second term i ...</math> games and lost <math>10</math> games; there were no ties. How many sets of three teams <math>\{A, B, C\}</math> were there in which <math>A</math>
  14 KB (2,037 words) - 19:09, 29 July 2023
• 1990 IMO Problems/Problem 4
  ...e non-trivial progress on this we must split all rational numbers into two sets, <math>S_1</math> and <math>S_2</math>, such that if <math>E \in S_1</math> ...into 2 and 1 mod 6 being in one set with 3 and 5 mod 6 in the other. These sets have equal sizes from a strong form of Dirichlet's theorem on arithmetic pr
  5 KB (1,045 words) - 11:01, 30 September 2022
• Axiom of choice
  ...a selection of exactly one object from each box, even if the collection is infinite. ...of choice says, given a set <math>S</math> of non-empty pairwise disjoint sets, there exists a set <math>X</math> with one element from each set in <math>
  1 KB (203 words) - 01:25, 12 January 2024
• 2019 Mock AMC 10B Problems/Problem 23
  ...ncrements per unit (this is because the maximum least value for one of the sets is <math>9</math>) such that no two of them overlap and (2) the number of w Since there are infinite real numbers in a unit of <math>1</math>, there are infinite increments in a unit of <math>1</math>, so we should take the limit as <mat
  2 KB (257 words) - 23:42, 29 November 2019
• Know the Facts: Gmaas
  ...oms, pocket dimensions, and many more fascinating things. The campus spans infinite miles into Gmaasia, all contained in pocket dimensions. Gmaas's room is in ...ft below ground level and filled it with dirt. The university temporarily sets itself up in a mansion in downtown Manhattan, and the university's artifact
  88 KB (14,928 words) - 13:54, 29 April 2024
• 1993 OIM Problems/Problem 6
  ...y of zeros and ones. Let <math>A</math> and <math>B</math> be two infinite sets of non-negative integers, such that <math>B</math> is the set of all number Prove that in one of the sets <math>A</math> or <math>B</math> there are infinitely many pairs of numbers
  686 bytes (118 words) - 14:22, 13 December 2023
• 2023 SSMO Team Round Problems
  ...ath>S = \{1, 2, 3, 4, \cdots, 23\}</math> and let there be randomly chosen sets <math>A, B, C</math> where <math>A, B, C \subseteq S</math>. The probabilit There exists a lane of infinite cars. Each car has a <math>\frac{1}{3}</math> chance of being high quality
  8 KB (1,238 words) - 02:14, 3 January 2024

View (previous 20 | next 20) (20 | 50 | 100 | 250 | 500)