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  • ...ity of <math>\{1, \{2, 3\}, \{1, 2, 3\}\}</math> is 3, and the cardinality of the [[empty set]] is 0. ...th> is denoted by <math>|A|</math>. In the above example, the cardinality of <math>\{3, 4\}</math> is <math>|\{3, 4\}| = 2</math>. Sometimes, the notati
    2 KB (263 words) - 23:54, 16 November 2019
  • ...ably infinite]]. The most common example of an uncountable set is the set of [[real number]]s <math>\mathbb{R}</math>. We give an [[indirect proof]] here. This is one of the most famous indirect proofs and was first given by [[Georg Cantor]].
    2 KB (403 words) - 19:53, 13 October 2019
  • ...we shall present just a brief discussion of the most common properties of sets and operations related to them. ...l it an [[infinite]] set. The objects in a set are called the [[element]]s of the set. A common misconception is that a set can have multiple indistinct
    11 KB (2,019 words) - 16:20, 7 July 2024
  • ...] <math>S</math> is the set <math>\mathcal{P}(S)</math> of all [[subset]]s of that set. It is also sometimes denoted by <math>2^S</math>. ...of the power set is strictly larger than the cardinality <math>|S|</math> of the set itself.
    4 KB (757 words) - 10:44, 8 March 2018
  • ...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) - 20:32, 13 August 2015