A set is said to be uncountable or uncountably infinite if it is infinite and cannot be placed into a one-to-one correspondence (i.e., a bijection) with the set of natural numbers. Georg Cantor proved that the set of real numbers is uncountable, a fact sometimes referred to as the “non-denumerability of the reals.”

Citation Info

  • [MLA] “uncountable.” Platonic Realms Interactive Mathematics Encyclopedia. Platonic Realms, 11 Apr 2014. Web. 19 Dec 2018. <>
  • [APA] uncountable (11 Apr 2014). Retrieved 19 Dec 2018 from the Platonic Realms Interactive Mathematics Encyclopedia:


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