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单词 Denumerable Set
释义

Denumerable Set

A 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.

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