The difference between Countably infinite and Denumerable

When used as adjectives, countably infinite means that is both countable and infinite, 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 Countably infinite and Denumerable

  1. Countably infinite as an adjective (set theory, of a set):

    That is both countable and infinite; having the same cardinality as the set of natural numbers; formally, such that a bijection exists from ℕ to the set.

  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."