✳flâneur — a map of the web's best reading

Well-ordering theorem - Wikipedia

en.wikipedia.org · 1,119 words · saved by 1 readers

In mathematics, the well-ordering theorem, also known as Zermelo's theorem, states that every set can be well-ordered. A set X is well-ordered by a strict total order if every non-empty subset of X has a least element under the ordering. The well-ordering theorem together with Zorn's lemma are the most important mathematical statements that are equivalent to the axiom of choice (often called AC, see also Axiom of choice § Equivalents).[1][2] Ernst Zermelo introduced the axiom of choice as an "unobjectionable logical principle" to prove the well-ordering theorem.[3] One can conclude from the well-ordering theorem that every set is susceptible to transfinite induction, which is considered by mathematicians to be a powerful technique.[3] One famous consequence of the theorem is the Banach–Tarski paradox. Georg Cantor considered the well-ordering theorem to be a "fundamental principle of thought".[4] However, it is considered difficult or even impossible to visualize a well-ordering of 𝑅

Well-ordering theorem - Wikipedia Jump to content From Wikipedia, the free encyclopedia Theorem that every set can be well-ordered "Zermelo's theorem" redirects here. For Zermelo's theorem in game theory, see Zermelo's theorem (game theory) . Not to be confused with Well-ordering principle . In mathematics , the well-ordering theorem , also known as Zermelo's theorem , states that every set can be well-ordered . A set X is well-ordered by a strict total order if every non-empty subset of X has a least element under the ordering. The well-ordering theorem together with Zorn's lemma are the most

Explore this link on the map →

related reading