1. well-ordering - Noun
2. well-ordering - Verb
well-ordering (plural well-orderings)
(mathematics) Synonym of well-order
well-ordering
present participle of well-order
A well-known joke alluding to this equivalency (which may defy human intuition) is attributed to Jerry Bona : "The Axiom of Choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?" citation. Source: Internet
Ernst Zermelo (1908) A new proof of the possibility of a well-ordering'' in van Heijenoort 1967:183–198. Source: Internet
In fact, Zermelo initially introduced the axiom of choice in order to formalize his proof of the well-ordering theorem. Source: Internet
Because there is no canonical well-ordering of all sets, a construction that relies on a well-ordering may not produce a canonical result, even if a canonical result is desired (as is often the case in category theory ). Source: Internet
Here is an account with fewer presuppositions: suppose that we associate with each well-ordering an object called its order type in an unspecified way (the order types are the ordinal numbers). Source: Internet
History Georg Cantor considered the well-ordering theorem to be a "fundamental principle of thought". Source: Internet