- NGC 6087 (Wikipedia)
NGC 6087 (also known as Caldwell 89 or the S Normae Cluster) is an open cluster of 40 or more stars centered on the Cepheid variable S Normae in the constellation Norma. At a distance of about 3500 ly and covering a field of almost one quarter of a degree, the stars range from seventh- to eleventh-magnitude, the brightest being 6.5 magnitude S Normae. The aggregate visual magnitude of the cluster is about 5.4.
- 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.