actual infinite

An infinite set or collection considered as a completed whole, for example the set \(ℕ=\{1,2,3,\ldots\}\) of natural numbers in modern set theory.

Aristotle, who theorized about infinity, distinguished the actually infinite from the potentially infinite. He believed that infinity could only exist as a potential, that to suppose an actual infinity led to logical contradictions. This teaching became a dogma that constrained mathematics for two millennia, until the development of set theory by Georg Cantor in the 1870’s.


  • B. Sidney Smith, author

Citation Info

  • [MLA] Smith, B. Sidney. "actual infinite." Platonic Realms Interactive Mathematics Encyclopedia. Platonic Realms, 8 Jun 2013. Web. 8 Jun 2013. <>
  • [APA] Smith, B. Sidney (8 Jun 2013). actual infinite. Retrieved 8 Jun 2013 from the Platonic Realms Interactive Mathematics Encyclopedia:


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