• Thumbnail for Infinite set
    In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable. The set of natural numbers (whose existence...
    8 KB (917 words) - 03:24, 10 May 2025
  • uncountable sets, that is, sets that are not countable; for example the set of the real numbers. Although the terms "countable" and "countably infinite" as defined...
    28 KB (4,381 words) - 01:01, 29 March 2025
  • Thumbnail for Infinity
    Infinity (redirect from The Infinite)
    infinity by studying infinite sets and infinite numbers, showing that they can be of various sizes. For example, if a line is viewed as the set of all of its...
    54 KB (6,115 words) - 21:45, 19 June 2025
  • In mathematics, a set A is Dedekind-infinite (named after the German mathematician Richard Dedekind) if some proper subset B of A is equinumerous to A...
    12 KB (1,751 words) - 15:44, 10 December 2024
  • Thumbnail for Set (mathematics)
    sets. A set may be finite or infinite. There is a unique set with no elements, called the empty set; a set with a single element is a singleton. Sets...
    49 KB (7,143 words) - 21:00, 7 July 2025
  • mathematics, an uncountable set, informally, is an infinite set that contains too many elements to be countable. The uncountability of a set is closely related...
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  • Thumbnail for Ordinal number
    set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, nth, etc.) aimed to extend enumeration to infinite...
    47 KB (6,689 words) - 14:57, 5 July 2025
  • Thumbnail for Union (set theory)
    B = {1, 2, 3, 4, 5, 6, 7}. A more elaborate example (involving two infinite sets) is: A = {x is an even integer larger than 1} B = {x is an odd integer...
    14 KB (1,967 words) - 08:46, 6 May 2025
  • (colloquial: Infinite Hotel Paradox or Hilbert's Hotel) is a thought experiment which illustrates a counterintuitive property of infinite sets. It is demonstrated...
    13 KB (2,131 words) - 15:16, 27 March 2025
  • the natural numbers form a set (necessarily infinite). A great discovery of Cantor is that, if one accepts infinite sets, then there are different sizes...
    19 KB (2,612 words) - 23:11, 9 July 2025
  • number) of the set. A set that is not a finite set is called an infinite set. For example, the set of all positive integers is infinite: { 1 , 2 , 3 ,...
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  • Thumbnail for Georg Cantor
    one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than...
    85 KB (10,164 words) - 19:54, 20 June 2025
  • of at least one infinite set, namely a set containing the natural numbers. It was first published by Ernst Zermelo as part of his set theory in 1908....
    11 KB (1,809 words) - 03:54, 21 June 2025
  • Thumbnail for Set theory
    of sets to mathematics. In his work, he (among other things) expanded on Galileo's paradox, and introduced one-to-one correspondence of infinite sets, for...
    54 KB (6,586 words) - 11:37, 29 June 2025
  • } where Z 0 {\displaystyle Z_{0}} is any infinite set and P {\displaystyle {\mathcal {P}}} is the power set operation. Moreover, one of Zermelo's axioms...
    46 KB (6,252 words) - 13:43, 7 June 2025
  • Thumbnail for Cardinal number
    a set. In the case of a finite set, its cardinal number, or cardinality is therefore a natural number. For dealing with the case of infinite sets, the...
    26 KB (3,834 words) - 18:49, 17 June 2025
  • Thumbnail for Power set
    countably infinite set is uncountably infinite. The power set of the set of natural numbers can be put in a one-to-one correspondence with the set of real...
    21 KB (2,479 words) - 08:24, 18 June 2025
  • contradictions within modern axiomatic set theory. Set theory as conceived by Georg Cantor assumes the existence of infinite sets. As this assumption cannot be...
    17 KB (2,657 words) - 12:12, 29 April 2025
  • quantify the size of infinite sets, and the transfinite ordinals, which are ordinal numbers used to provide an ordering of infinite sets. The term transfinite...
    10 KB (1,232 words) - 08:58, 23 October 2024
  • cardinality of set B and set C are both 3. An infinite set is a set with an infinite number of elements, while a finite set is a set with a finite number...
    8 KB (1,031 words) - 00:32, 11 July 2025
  • Thumbnail for Cardinality
    Cardinality (redirect from Set modulus)
    property of sets, roughly meaning the number of individual objects they contain, which may be infinite. The cardinal number corresponding to a set A {\displaystyle...
    81 KB (10,754 words) - 00:31, 11 July 2025
  • Thumbnail for Aleph number
    particularly in set theory, the aleph numbers are a sequence of numbers used to represent the cardinality (or size) of infinite sets. They were introduced...
    17 KB (2,453 words) - 10:45, 21 June 2025
  • Thumbnail for Cantor set
    Cantor ternary set contains all points in the interval [ 0 , 1 ] {\displaystyle [0,1]} that are not deleted at any step in this infinite process. The same...
    42 KB (6,396 words) - 08:11, 16 June 2025
  • Look up infinite in Wiktionary, the free dictionary. Infinite may refer to: Infinite set, a set that is not a finite set Infinity, an abstract concept...
    2 KB (209 words) - 06:12, 12 June 2024
  • Thumbnail for Infinite dihedral group
    two-dimensional geometry, the infinite dihedral group represents the frieze group symmetry, p1m1, seen as an infinite set of parallel reflections along...
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  • Thumbnail for Infinite monkey theorem
    The infinite monkey theorem states that a monkey hitting keys independently and at random on a typewriter keyboard for an infinite amount of time will...
    53 KB (7,044 words) - 22:38, 19 June 2025
  • Thumbnail for Empty set
    infinity, which guarantees the existence of at least one infinite set, can be used to construct the set of natural numbers, N 0 {\displaystyle \mathbb {N} _{0}}...
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  • Thumbnail for Symmetric group
    ! {\displaystyle n!} . Although symmetric groups can be defined on infinite sets, this article focuses on the finite symmetric groups: their applications...
    46 KB (6,212 words) - 00:39, 20 June 2025
  • denumerably infinite. This is not, in fact, a theorem of mathematics. But, according to Hartman, people are capable of a denumerably infinite set of predicates...
    5 KB (677 words) - 05:33, 27 August 2024
  • In set theory, an amorphous set is an infinite set which is not the disjoint union of two infinite subsets. Amorphous sets cannot exist if the axiom of...
    5 KB (673 words) - 05:35, 24 June 2025