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 is given, any other set which can be put into a One-to-One correspondence with 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
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.