# 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

- [MLA] Smith, B. Sidney. "actual infinite."
*Platonic Realms Interactive Mathematics Encyclopedia.*Platonic Realms, 8 Jun 2013. Web. 8 Jun 2013. <http://platonicrealms.com/> - [APA] Smith, B. Sidney (8 Jun 2013). actual infinite. Retrieved 8 Jun 2013 from the
*Platonic Realms Interactive Mathematics Encyclopedia:*http://platonicrealms.com/encyclopedia/actual-infinite/