Word.ws English Dictionary

countably infinite

countably infinite adjective: 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.

Adjective

countably infinite (not comparable)

  1. 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.
    • 1953 [Addison-Wesley], Bruce Elwyn Meserve, Fundamental Concepts of Algebra, 1982, Dover, page 36,
      This one-to-one correspondence between the set of positive integers and the set of pairs of positive integers indicates that the set of pairs is countably infinite. Since the set of positive rational...
    • Instead of saying that the aggregate of natural numbers is countably infinite (see Chapter 24), one can use Cantor's symbolism and state that its cardinal number is #92;aleph#95;0 (read aleph null).[…]Now the range of a random variable may be a finite set, a countably infinite set, or a continuum.1970, Edna E. Kramer, “The Nature and Growth of Modern Mathematics”, in Paperback, Princeton University Press, published 1982, page 332

Questions about countably infinite

What does countably infinite mean?
Countably infinite means 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.
What part of speech is countably infinite?
Countably infinite is an adjective.

Words near countably infinite in the dictionary

  1. countable sets
  2. countableness
  3. countables
  4. countably
  5. countably additive
  6. countably infinite
  7. countback
  8. countbacks
  9. countdom
  10. countdoms
  11. countdown

Source and license

Adapted from Wiktionary: countably infinite (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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