In set theory, a continuous function is a sequence of ordinals such that the values assumed at limit stages are the limits (limit suprema and limit infima) of all values at previous stages.
More formally, let γ be an ordinal, and
Then s is continuous if at every limit ordinal β < γ, and Alternatively, if s is an increasing function then s is continuous if s: γ → range(s) is a continuous function when the sets are each equipped with the order topology.
These continuous functions are often used in cofinalities and cardinal numbers.
This mathematical logic-related article is a stub.