An ordinal number 
is called a limit ordinal iff
it has no immediate predecessor, i.e., if there is
no ordinal number 
such that 
(Ciesielski 1997, p. 46; Moore 1982, p. 60;
Rubin 1967, p. 182; Suppes 1972, p. 196). The first limit ordinal is 
.
Limit Ordinal
See also
Ordinal Number, SuccessorExplore with Wolfram|Alpha
References
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.Referenced on Wolfram|Alpha
Limit OrdinalCite this as:
Weisstein, Eric W. "Limit Ordinal." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LimitOrdinal.html