Editing Cofinality (section)

==Properties==

If <math>A</math> admits a [[total order|totally ordered]] cofinal subset, then we can find a subset <math>B</math> that is well-ordered and cofinal in <math>A.</math> Any subset of <math>B</math> is also well-ordered. Two cofinal subsets of <math>B</math> with minimal cardinality (that is, their cardinality is the cofinality of <math>B</math>) need not be order isomorphic (for example if <math>B = \omega + \omega,</math> then both <math>\omega + \omega</math> and <math>\{\omega + n : n < \omega\}</math> viewed as subsets of <math>B</math> have the countable cardinality of the cofinality of <math>B</math> but are not order isomorphic).  But cofinal subsets of <math>B</math> with minimal order type will be order isomorphic.