Equipotent Sets

Equipotent Sets

Sets that can be put in a one-to-one relation with one another.


Sets A and B below are equipotent.


  • 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 numbers is called countably infinite sets. This is the case for \(\mathbb{Z}\) and \(\mathbb{Q}\), for example. The set of real numbers is a countably infinite set.

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