Denumerable Set

A Set is denumerable if a prescription can be given for identifying its members one at a time. Such a set is said to have Cardinal Number Aleph-0. Examples of denumerable sets include Algebraic Numbers, Integers, and Rational Numbers. Once one denumerable set $S$ is given, any other set which can be put into a One-to-One correspondence with $S$ is also denumerable. Examples of nondenumerable sets include the Real, Complex, Irrational, and Transcendental Numbers.

See also Aleph-0, Aleph-1, Cantor Diagonal Slash, Continuum, Hilbert Hotel

References

Courant, R. and Robbins, H. ``The Denumerability of the Rational Number and the Non-Denumerability of the Continuum.'' §2.4.2 in What is Mathematics?: An Elementary Approach to Ideas and Methods, 2nd ed. Oxford, England: Oxford University Press, pp. 79-83, 1996.