A set is denumerable iff it is equipollent to the finite ordinal numbers. (Moore 1982, p. 6; Rubin 1967, p. 107; Suppes 1972, pp. 151-152). However, Ciesielski (1997, p. 64) calls this property "countable." The set aleph0 is most commonly called "denumerable" to "countably infinite".
Denumerable Set
See also
Countable Set, Countably InfiniteExplore with Wolfram|Alpha
References
Ciesielski, K. Set Theory for the Working Mathematician. Cambridge, England: Cambridge University Press, 1997.Dauben, J. W. Georg Cantor: His Mathematics and Philosophy of the Infinite. Princeton, NJ: Princeton University Press, 1990.Ferreirós, J. "Non-Denumerability of
."
§6.2 in Labyrinth
of Thought: A History of Set Theory and Its Role in Modern Mathematics. Basel,
Switzerland: Birkhäuser, pp. 177-183, 1999.Moore, G. H.
Zermelo's
Axiom of Choice: Its Origin, Development, and Influence. New York: Springer-Verlag,
1982.Rubin, J. E. Set
Theory for the Mathematician. New York: Holden-Day, 1967.Suppes,
P. Axiomatic
Set Theory. New York: Dover, 1972.Referenced on Wolfram|Alpha
Denumerable SetCite this as:
Weisstein, Eric W. "Denumerable Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DenumerableSet.html