释义 |
Denumerable SetA Set is denumerable if a prescription can be given for identifying its members one at a time. Such a set is saidto have Cardinal Number Aleph-0. Examples of denumerable sets include AlgebraicNumbers, Integers, and Rational Numbers. Once onedenumerable set is given, any other set which can be put into a One-to-One correspondence with is alsodenumerable. 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. |