denumerable

Capable of being assigned a bijection to the natural numbers. Applied to sets which are not finite, but have a one-to-one mapping to the natural numbers.

Adjective

  1. Capable of being assigned a bijection to the natural numbers. Applied to sets which are not finite, but have a one-to-one mapping to the natural numbers.
    • The empty set is not denumerable because it is finite; the rational numbers are, surprisingly, denumerable because every possible fraction can be assigned a natural number and vice versa.

    Synonyms: countable countably infinite

Origin

The word was introduced around the beginning of the 20th century, from Latin denumerō (“to count out”) + -able.

Related

countable set uncountable set enumerable

Derived

denumerability denumerably indenumerable nondenumerable non-denumerable