• 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...
    12 KB (1,882 words) - 17:26, 22 September 2024
  • 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...
    7 KB (989 words) - 17:35, 14 March 2024
  • In mathematics, the well-ordering principle states that every non-empty subset of nonnegative integers contains a least element. In other words, the set...
    7 KB (1,144 words) - 09:34, 17 August 2024
  • 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...
    18 KB (3,049 words) - 11:59, 22 May 2024
  • 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...
    10 KB (1,382 words) - 15:55, 4 November 2024
  • lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences...
    23 KB (3,352 words) - 07:24, 16 November 2023
  • 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 ≤...
    21 KB (3,093 words) - 12:07, 5 October 2024
  • ∗ {\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...
    5 KB (695 words) - 12:50, 4 September 2024
  • Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing...
    31 KB (4,508 words) - 03:55, 24 August 2024
  • Thumbnail for Ordinal number
    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...
    48 KB (6,712 words) - 03:10, 2 November 2024
  • Thumbnail for Transfinite induction
    transfinite induction: First, well-order the real numbers (this is where the axiom of choice enters via the well-ordering theorem), giving a sequence ⟨...
    8 KB (1,142 words) - 11:05, 24 October 2024
  • 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...
    32 KB (4,072 words) - 08:28, 1 November 2024
  • Thumbnail for Monotonic function
    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,...
    19 KB (2,467 words) - 04:06, 27 August 2024
  • Thumbnail for Partially ordered set
    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....
    40 KB (5,388 words) - 19:57, 4 November 2024
  • Thumbnail for Georg Cantor
    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...
    83 KB (10,020 words) - 21:06, 5 November 2024
  • Thumbnail for Law & Order: Special Victims Unit
    2024, Law & Order: Special Victims Unit has aired 557 original episodes, well surpassing the episode count of the original Law & Order series. In terms...
    153 KB (11,353 words) - 04:49, 8 November 2024
  • and Boolean algebras. These lattice-like structures all admit order-theoretic as well as algebraic descriptions. The sub-field of abstract algebra that...
    40 KB (5,665 words) - 11:17, 1 November 2024
  • Thumbnail for Preorder
    Preorder (redirect from Quasi-order)
    In mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. The name preorder is meant...
    23 KB (3,351 words) - 13:50, 21 July 2024
  • Thumbnail for Order of Australia
    The Order of Australia is an Australian honour that recognises Australian citizens and other persons for outstanding achievement and service. It was established...
    57 KB (4,728 words) - 01:25, 3 November 2024
  • Thumbnail for Order of the British Empire
    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...
    59 KB (5,979 words) - 08:05, 6 November 2024
  • In the mathematical field of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism...
    7 KB (997 words) - 20:41, 15 December 2022
  • {\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...
    32 KB (6,092 words) - 05:10, 28 August 2024
  • Kruskal's tree theorem (category Order theory)
    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...
    14 KB (1,819 words) - 22:33, 21 October 2024
  • Thumbnail for Axiom of choice
    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...
    58 KB (7,685 words) - 23:16, 6 November 2024
  • Thumbnail for Mathematical induction
    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...
    47 KB (6,855 words) - 17:50, 24 October 2024
  • Thumbnail for Weak ordering
    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...
    30 KB (4,360 words) - 12:57, 6 October 2024
  • Thumbnail for Illuminati
    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...
    55 KB (7,160 words) - 21:41, 24 October 2024
  • 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...
    14 KB (2,091 words) - 18:28, 15 October 2024
  • Thumbnail for Wells Fargo
    Consumer Protection Act". Congress.gov. "2022-CFPB-0011_Wells Fargo Bank N.A. - Consent Order" "Deadwood Stage (Whip Crack Away, Calamity Jane) Lyrics"...
    94 KB (8,450 words) - 04:30, 29 October 2024
  • Thumbnail for Order of Canada
    as well as efforts by non-Canadians who have made the world better by their actions. Membership is accorded to those who exemplify the order's Latin...
    61 KB (6,328 words) - 08:11, 23 October 2024