deNumer

Denumer is an English mathematical verb meaning to establish a denumeration of a set: to show that its elements can be placed in a one-to-one correspondence with the natural numbers. When such a correspondence exists, the set is said to be denumerable (also called countable). The noun form denumeration denotes the act of performing this process.

Usage: To denumer a set is to construct a bijection f: N → S or an explicit listing that assigns a unique natural number to each element of S. This demonstrates that S is denumerable. Examples include N itself; the set of even integers; and the set of rational numbers, all of which are denumerable though the constructions vary in complexity.

Etymology and usage notes: The term denumer is rare and primarily historical; modern texts prefer denumerable or countable, or the verb enumerate for listing elements without asserting a bijection. See also denumerable, countable set, bijection, natural numbers.