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.