Limit Ordinal

An ordinal number alpha>0 is called a limit ordinal iff it has no immediate predecessor, i.e., if there is no ordinal number beta such that beta+1=alpha (Ciesielski 1997, p. 46; Moore 1982, p. 60; Rubin 1967, p. 182; Suppes 1972, p. 196). The first limit ordinal is omega.

See also

Ordinal Number, Successor

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Ciesielski, K. Set Theory for the Working Mathematician. Cambridge, England: Cambridge University Press, 1997.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.

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Limit Ordinal

Cite this as:

Weisstein, Eric W. "Limit Ordinal." From MathWorld--A Wolfram Web Resource.

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