The difference between Countable and Denumerable

When used as adjectives, countable means capable of being counted, whereas denumerable means 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.


check bellow for the other definitions of Countable and Denumerable

  1. Countable as an adjective:

    Capable of being counted; having a quantity.

  2. Countable as an adjective (mathematics, of a set):

    Finite or countably infinite; having a one-to-one correspondence (bijection) with a subset of the natural numbers.

  3. Countable as an adjective (mathematics, of a set):

    Countably infinite; having a bijection with the natural numbers.

  4. Countable as an adjective (grammar, of a noun):

    Freely usable with the indefinite article and with numbers, and therefore having a plural form.

  1. Denumerable as an adjective (mathematics):

    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.

    Examples:

    "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."