- Messier 58 (Wikipedia)
Messier 58 (also known as M58 and NGC 4579) is an intermediate barred spiral galaxy with a weak inner ring structure located within the constellation Virgo, approximately 68 million light-years away from Earth. It was discovered by Charles Messier on April 15, 1779 and is one of four barred spiral galaxies that appear in Messier’s catalogue. M58 is one of the brightest galaxies in the Virgo Cluster. From 1779 it was arguably (though unknown at that time) the farthest known astronomical object until the release of the New General Catalogue in the 1880s and even more so the publishing of redshift values in the 1920s.
- 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.