numerabilis

Numerabilis is a Latin adjective meaning “able to be counted” or “countable.” In historical and modern Neo-Latin usage, it is used to describe objects, sets, or phenomena that can be enumerated or assigned a one-to-one correspondence with the natural numbers. The form derives from numerare, “to count,” with the suffix -abilis, “able to be.”

In mathematics, numerabilis is often rendered in English as “countable” or “denumerable.” A set is numerabilis if either finite or countably infinite; equivalently, there exists a bijection between the set and the natural numbers. By contrast, uncountable sets (such as the real numbers) are not numerabilis. The Latin term appears primarily in Latin-language texts and in discussions of historical logical and mathematical doctrines, where scholars translate the standard concept of countability into Latin.

Beyond pure mathematics, numerabilis can appear in philosophy or linguistics to describe phenomena that can be enumerated or listed in principle, such as a numerabilis collection of instances or examples, though this usage is less formal and varies by author.

In modern usage, numerabilis is not a common term in contemporary mathematical discourse, where “countable” is preferred in English and in languages using the Latin-derived terms have their own equivalents. Nevertheless, numerabilis remains a recognizable Neo-Latin form for discussions of countability in historical or multilingual contexts.

See also: Countable, Denumerable, Finite, Cardinality, Set theory.