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@Fried_Brice @tjohnhos Yeah. If α<β and the range of some f:α→β has no upper bound in β, then β is non-regular. Put another way, regular means that every copy of a smaller cardinal inside it is bounded above. This gets us nice results that generalize the notion of countable vs uncountable.Permalink On twitter.com
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@Fried_Brice @tjohnhos So if β is regular, then the union of <β sets each of cardinality <β is still <β. Thinking a beat more, that's a better characterization than the one I paraphrased above.On twitter.com