well-founded order | well order

A totally ordered set (A, <=) is said to be well ordered (or have a well-founded order) iff every nonempty subset of A has a least element. Every finite totally ordered set is well ordered. The set of integers Z, which has no least element, is an example of a set that is not well ordered. An ordinal number is the order type of a well ordered set.

axiom of choice | Hilbert's problems | initial segment | monomial order | order type | ordinal number | subset | well ordering principle