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In Studies in Logic and the Foundations of Mathematics, 2000. 1.5.3 Denumerable partition of the continuum. Let a be a set equipotent with the continuum. For every partition of a into denumerably many subsets, one of the subsets is equipotent with the continuum (uses the axiom of choice). • Suppose on the contrary that there is a partition of a into disjoint subsets a i (i integer), and that ... Visit website
Properties. Two sets are equipotent if and only if they have the same cardinal. Two infinite sets can have different cardinals if they are not equipotent. Therefore, the set of whole numbers, which is an infinite set, does not have the same cardinality as the set of real numbers. All of the infinite sets that are equipotent to the set of whole ... Visit website
Equipotent definition, equal in power, ability, or effect. See more. Visit website
Equipotence and non-empty sets Thread starter jetoso; Start date Sep 21, 2007; Sep 21, 2007 #1 jetoso. 73 0. Hello, I am trying to prove the following about equipotence: Let A and B be nonempty sets. We say that A is equipotent with B if there is a bijection between A and B. Then the following hold: Visit website