Bounded (set theory)

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In set theory a subset X of a limit ordinal λ is said to be bounded if its supremum is less than λ. If it is not bounded, it is unbounded, that is

$\sup(X)= \lambda.\,$

For functions, bounded or unboundedness refers to the range of the function when considered as a subset of the codomain.

[edit] See also

Club set

[edit] References

Jech, Thomas, 2003. Set Theory: The Third Millennium Edition, Revised and Expanded. Springer. ISBN 3-540-44085-2.
Kunen, Kenneth, 1980. Set Theory: An Introduction to Independence Proofs. Elsevier. ISBN 0-444-86839-9.