cofinality

Noun

Meaning

(mathematics, countable) The least of the cardinalities of the cofinal subsets of a partially ordered set.
The cofinality of any set with a greatest element is 1.

(mathematics, uncountable) The property of being cofinal.

Examples

Examples * The cofinality of a partially ordered set with greatest element is 1 as the set consisting only of the greatest element is cofinal (and must be contained in every other cofinal subset). Source: Internet

In 1904 Hausdorff published the recursion named after him: For each non-limit ordinal we have This formula was, together with the later notion of cofinality introduced by Hausdorff, the basis for all further results for Aleph exponentiation. Source: Internet

If two cofinal subsets of B have minimal cardinality (i.e. their cardinality is the cofinality of B), then they are order isomorphic to each other. Source: Internet

Of fundamental importance to the whole theory is the concept of cofinality that Hausdorff introduced. Source: Internet

The cofinality of 0 is 0. The cofinality of any successor ordinal is 1. The cofinality of any nonzero limit ordinal is an infinite regular cardinal. Source: Internet

The cofinality of a set of ordinals or any other well-ordered set is the cofinality of the order type of that set. Source: Internet

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