- Beta Gruis (β Gruis, abbreviated Beta Gru, β Gru), formally named Tiaki /tiˈɑːki/, is the second brightest star in the southern constellation of Grus. It was once considered the rear star in the tail of the constellation of the (Southern) Fish, Piscis Austrinus: it, with Alpha, Delta, Theta, Iota, and Lambda Gruis, belonged to Piscis Austrinus in medieval Arabic astronomy.
- Well-ordering theorem (Wikipedia)
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). Ernst Zermelo introduced the axiom of choice as an “unobjectionable logical principle” to prove the well-ordering theorem. 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. One famous consequence of the theorem is the Banach–Tarski paradox.