In mathematics, a well-order (or well-ordering or well-order relation) on a set S is a total ordering on S with the property that every non-empty subset...

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...

In mathematics, the well-ordering principle states that every non-empty subset of nonnegative integers contains a least element. In other words, the set...

In mathematics, specifically order theory, a well-quasi-ordering or wqo on a set X {\displaystyle X} is a quasi-ordering of X {\displaystyle X} for which...

In order theory, a partial order is called well-founded if the corresponding strict order is a well-founded relation. If the order is a total order then...

mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation ≤...

lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences...

∗ {\displaystyle \sigma ^{*}} . The order type of a well-ordered set X is sometimes expressed as ord(X). The order type of the integers and rationals is...

Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing...

transfinite induction: First, well-order the real numbers (this is where the axiom of choice enters via the well-ordering theorem), giving a sequence ⟨...

linear order such that every non-empty subset has a least element is called a well-order. The axiom of choice implies that every set can be well-ordered...

New World Order is a non-fiction book written by H.G. Wells and was published by Secker & Warburg in January 1940. In The New World Order, Wells proposed...

or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus,...

In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other....

natural numbers. It begins by defining well-ordered sets. Ordinal numbers are then introduced as the order types of well-ordered sets. Cantor then defines...

2024, Law & Order: Special Victims Unit has aired 557 original episodes, well surpassing the episode count of the original Law & Order series. In terms...

The Most Excellent Order of the British Empire is a British order of chivalry, rewarding contributions to the arts and sciences, work with charitable and...

and Boolean algebras. These lattice-like structures all admit order-theoretic as well as algebraic descriptions. The sub-field of abstract algebra that...

In mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. The name preorder is meant...

The Order of Australia is an Australian honour that recognises Australian citizens and other persons for outstanding achievement and service. It was established...

In the mathematical field of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism...

{\displaystyle L} . It is well known that the axiom of choice is equivalent to the ability to well-order every set. Being able to well-order the proper class V...

states: If X is well-quasi-ordered, then the set of rooted trees with labels in X is well-quasi-ordered under the inf-embeddable order defined above. (That...

choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering theorem. In many cases, a set created by choosing...

n):n\in \mathbb {N} \}} , shown in the picture, is well-ordered: 35lf  by the lexicographic order. Moreover, except for the induction axiom, it satisfies...

In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose...

religious influence over public life, and abuses of state power. "The order of the day," they wrote in their general statutes, "is to put an end to...

is called orderable or linearly orderable if there exists a total order on its elements such that the order topology induced by that order and the given...

order relations on the set of monomials that are not well-orders. In the case of finitely many variables, well-ordering of a monomial order is equivalent...

Consumer Protection Act". Congress.gov. "2022-CFPB-0011_Wells Fargo Bank N.A. - Consent Order" "Deadwood Stage (Whip Crack Away, Calamity Jane) Lyrics"...