Zorn may refer to:
In mathematics, the Hausdorff maximal principle is an alternate and earlier formulation of Zorn's lemma proved by Felix Hausdorff in 1914. It states that in any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset, where "maximal" is with respect to set inclusion.
In mathematics and other fields, a lemma is a generally minor, proven proposition which is used to prove a larger statement. For that reason, it is also known as a "helping theorem" or an "auxiliary theorem". In many cases, a lemma derives its importance from the theorem it aims to prove; however, a lemma can also turn out to be more important than originally thought.
Max August Zorn was a German mathematician. He was an algebraist, group theorist, and numerical analyst. He is best known for Zorn's lemma, a method used in set theory that is applicable to a wide range of mathematical constructs such as vector spaces, and ordered sets amongst others. Zorn's lemma was first postulated by Kazimierz Kuratowski in 1922, and then independently by Zorn in 1935.
Kazimierz Kuratowski was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics. He worked as a professor at the University of Warsaw and at the Mathematical Institute of the Polish Academy of Sciences. Between 1946 and 1953, he served as President of the Polish Mathematical Society.
Zorn's lemma, also known as the Kuratowski–Zorn lemma, is a proposition of set theory. It states that a partially ordered set containing upper bounds for every chain necessarily contains at least one maximal element.
An in-joke, also known as an inside joke or a private joke, is a joke with humour that is understandable only to members of an ingroup; that is, people who are in a particular social group, occupation, or other community of shared interest. It is, therefore, an esoteric joke, only humorous to those who are aware of the circumstances behind it.
In mathematics, the Boolean prime ideal theorem states that ideals in a Boolean algebra can be extended to prime ideals. A variation of this statement for filters on sets is known as the ultrafilter lemma. Other theorems are obtained by considering different mathematical structures with appropriate notions of ideals, for example, rings and prime ideals, or distributive lattices and maximal ideals. This article focuses on prime ideal theorems from order theory.
In mathematics, Chow's theorem may refer to a number of theorems due to Wei-Liang Chow:
Tor, TOR or ToR may refer to:
ZL may refer to:
Gauss's lemma can mean any of several mathematical lemmas named after Carl Friedrich Gauss:
Lemma may refer to:
In mathematics, Weyl's theorem or Weyl's lemma might refer to one of a number of results of Hermann Weyl. These include
In mathematics, and more specifically in ring theory, Krull's theorem, named after Wolfgang Krull, asserts that a nonzero ring has at least one maximal ideal. The theorem was proved in 1929 by Krull, who used transfinite induction. The theorem admits a simple proof using Zorn's lemma, and in fact is equivalent to Zorn's lemma, which in turn is equivalent to the axiom of choice.
Aubin may refer to:
Jerry Lloyd Bona is an American mathematician, known for his work in fluid mechanics, partial differential equations, and computational mathematics, and active in some other branches of pure and applied mathematics.
At least three well-known results in mathematics bear the name Schur's lemma:
In order theory, the Szpilrajn extension theorem, proved by Edward Szpilrajn in 1930, states that every partial order is contained in a total order. Intuitively, the theorem says that any method of comparing elements that leaves some pairs incomparable can be extended in such a way that every pair becomes comparable. The theorem is one of many examples of the use of the axiom of choice in the form of Zorn's lemma to find a maximal set with certain properties.