When we think of infinity we usually think of the usual two categorical distinctions: a potential infinite and an actual infinite. A potential infinite suggests that infinity is only an idea or a concept but doesn’t actually exist in the Platonic sense or in the physical sense. In any set, one may always be added. An actual infinite is the notion that there exists such a set, Platonic or physical, which*is* infinite. A potential infinity may be symbolized by a lemniscate: ∞. An actual infinite can be depicted by the aleph-null or aleph-nought: ℵ0 (The Hebrew letter aleph with a subscript zero).

First, let’s have a brief refresher on set theory. A set is any collection of things or numbers that belong to a well-defined category. In a set notation, this would be written as {2, 3, 5, 7, 11} being the first five prime numbers, which is a finite set of things. Let’s simply signify this set as S. There is a proper subset (SS) of S. There are members in S that are not in SS, but no member of SS that is not in S.