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Class of mathematical orderings
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
Well-order
Generalised alphabetical order
lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences
Lexicographic_order
Statement that all non empty subsets of positive numbers contains a least element
In mathematics, the well-ordering principle, also called the well-ordering property or least natural number principle, states that every non-empty subset
Well-ordering_principle
Theorem that every set can be well-ordered
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
Well-ordering_theorem
Mathematical concept for comparing objects
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
Well-quasi-ordering
Order whose elements are all comparable
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 ≤
Total_order
Type of binary relation
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
Well-founded_relation
Generalization of "n-th" to infinite cases
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
Ordinal_number
Order-preserving mathematical 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,
Monotonic_function
Mathematician (1845–1918)
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
Georg_Cantor
Mathematical set with an ordering
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.
Partially_ordered_set
British order of chivalry established in 1917
The Most Excellent Order of the British Empire is a British order of chivalry, rewarding valuable service in a wide range of useful activities. It comprises
Order_of_the_British_Empire
Isomorphism type of ordered sets
∗ {\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_type
Branch of mathematics
Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing
Order_theory
Order for the terms of a polynomial
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
Monomial_order
denoted property (K) Well-founded relation Ordinal number Well-quasi-ordering Semilattice Lattice (Directed) complete partial order, (d)cpo Bounded complete
List_of_order_theory_topics
Reflexive and transitive binary relation
In mathematics, in particular in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive. The name preorder is meant
Preorder
In order-theoretic mathematics, a series-parallel partial order is a partially ordered set built up from smaller series-parallel partial orders by two
Series-parallel_partial_order
American television series (1999–present)
2026, Law & Order: Special Victims Unit has aired 594 original episodes, well surpassing the episode count of the original Law & Order series. In terms
Law & Order: Special Victims Unit
Law_&_Order:_Special_Victims_Unit
Certain topology in mathematics
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_topology
Construction in order theory
B} , respectively, the product order (also called the coordinatewise order or componentwise order) is a partial order ≤ {\displaystyle \leq } on the Cartesian
Product_order
Nonempty, upper-bounded, downward-closed subset
In mathematical order theory, an ideal is a special subset of a partially ordered set (poset). Although this term historically was derived from the notion
Ideal_(order_theory)
Mathematical ranking of a set
In order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with
Weak_ordering
Term in the mathematical area of order theory
In the mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted
Duality_(order_theory)
Existence of certain infima or suprema of a given poset
In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset)
Completeness_(order_theory)
Well-quasi-ordering of finite trees
Feferman–Schütte ordinal, is well-founded; in particular, the inf-embeddable ordering on a countable label set contains a well-ordered chain of order type Γ 0 {\displaystyle
Kruskal's_tree_theorem
1940 non-fiction book by H. G. Wells
New World Order is a non-fiction book written by H. G. Wells and published by Secker & Warburg in January 1940. In The New World Order, Wells proposes
The New World Order (Wells book)
The_New_World_Order_(Wells_book)
On chains and antichains in partial orders
In mathematics, in the areas of order theory and combinatorics, Dilworth's theorem states that, in any finite partially ordered set, the maximum size
Dilworth's_theorem
incomparabilities) Well-orders, total orders in which every non-empty subset has a least element Well-quasi-orderings, a class of preorders generalizing the well-orders
List of order structures in mathematics
List_of_order_structures_in_mathematics
Glossary of terms used in branch of mathematics
related to the fields of order, lattice, and domain theory. Note that there is a structured list of order topics available as well. Other helpful resources
Glossary_of_order_theory
Mathematical concept
principle is also true for arbitrary well-ordered sets, but since any well-ordered set can be indexed by ordinals in an order-preserving way, it suffices to
Transfinite_induction
Australian national honour
The Order of Australia is an Australian honour which recognises Australian citizens and other persons for outstanding service and achievement. It was
Order_of_Australia
Mathematical system
arithmetic. Unlike Peano arithmetic, second-order arithmetic allows quantification over sets of natural numbers as well as numbers themselves. Because real numbers
Second-order_arithmetic
Algebraic object with an ordered structure
In mathematics, an ordered field is a field together with a total ordering of its elements that is compatible with the field operations. Basic examples
Ordered_field
In mathematics, especially order theory, a prefix ordered set generalizes the intuitive concept of a tree by introducing the possibility of continuous
Prefix_order
Measure of how well someone's life is going
temporal order of episodes of well-being matters. Welfare biology, a related field, examines whether all sentient beings are capable of well-being, under
Well-being
Equivalence of partially ordered sets
In the mathematical field of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism
Order_isomorphism
Concept in order theory
In mathematics, specifically order theory, the join of a subset S {\displaystyle S} of a partially ordered set P {\displaystyle P} is the supremum (least
Join_and_meet
Type of monotone function
other hand, it might well be that two (necessarily infinite) posets are mutually order-embeddable into each other without being order-isomorphic. An example
Order_embedding
Topology of an ordered vector space
In mathematics, specifically in order theory and functional analysis, the order topology of an ordered vector space ( X , ≤ ) {\displaystyle (X,\leq )}
Order topology (functional analysis)
Order_topology_(functional_analysis)
this preorder is even a partial order (called the specialization order). On the other hand, for T1 spaces the order becomes trivial and is of little
Specialization_preorder
better-quasi-ordering is a well-quasi-ordering. Though well-quasi-ordering is an appealing notion, many important infinitary operations do not preserve well-quasi-orderedness
Better-quasi-ordering
Mathematical ordering of a partial order
In order theory, a branch of mathematics, a linear extension of a partial order is a total order (or linear order) that is compatible with the partial
Linear_extension
18th-century Bavarian secret society
influence over public life, and abuses of state power by monarchs. "The order of the day", they wrote in their general statutes, "is to put an end to
Illuminati
Set whose pairs have minima and maxima
geometric lattices (matroids). These lattice-like structures all admit order-theoretic as well as algebraic descriptions. The sub-field that studies lattices
Lattice_(order)
Type of ordering of a set
In mathematics, a partial order or total order < on a set X {\displaystyle X} is said to be dense if, for all x {\displaystyle x} and y {\displaystyle
Dense_order
Standard system of axiomatic set theory
"definite" property as one that could be formulated as a well-formed formula in a first-order logic whose atomic formulas were limited to set membership
Zermelo–Fraenkel_set_theory
Ordinals in mathematics and set theory
is to say that a computable ordinal is the order-type of some recursive (i.e., computable) well-ordering of the natural numbers; so, essentially, an
Large_countable_ordinal
Vector space with a partial order
partially ordered vector space is a real vector space equipped with a partial order that is compatible with the vector space operations. Given a vector space
Ordered_vector_space
British order of chivalry established in 1725
The Most Honourable Order of the Bath is a British order of chivalry founded by King George I on 18 May 1725. Recipients of the Order are usually senior
Order_of_the_Bath
Special type of lattice
can choose to consider a distributive lattice L either as a structure of order theory or of universal algebra. Both views and their mutual correspondence
Distributive_lattice
Property of a relation on a set
linear) order is a partial order in which any two elements are comparable; that is, the order relation is connected. Similarly, a strict partial order that
Connected_relation
Subset of incomparable elements
In mathematics, in the area of order theory, an antichain is a subset of a partially ordered set such that any two distinct elements in the subset are
Antichain
Well drilled to extract crude oil and/or gas
associated petroleum gas along with the oil. A well that is designed to produce only gas may be termed a gas well. Wells are created by drilling down into an oil
Oil_well
Mathematical result or axiom on order relations
the set of all chains in P {\displaystyle P} . By the well-ordering theorem, we find a well-ordering ⪯ {\displaystyle \preceq } on P {\displaystyle P} .
Hausdorff_maximal_principle
Form of mathematical proof
\{(1,n):n\in \mathbb {N} \}} , shown in the picture, is well-ordered by the lexicographic order. Moreover, except for the induction axiom, it satisfies
Mathematical_induction
American television series (1990–2010, 2022–present)
by Jury, Law & Order: LA, Law & Order True Crime, and Law & Order: Organized Crime) as well as a television film (Exiled: A Law & Order Movie). The commercial
Law_&_Order
Alternative mathematical ordering
mathematics, a cyclic order is a way to arrange a set of objects in a circle.[nb] Unlike most structures in order theory, a cyclic order is not modeled as
Cyclic_order
Medieval military order
crusading military order for supporting Catholic rule in the Holy Land and the Northern Crusades during the Middle Ages, as well as supplying military
Teutonic_Order
Smallest ordinal number that, considered as a set, is uncountable
{\displaystyle \Omega } , is the smallest ordinal number that is the order type of an uncountable well-ordered set. It is the supremum (least upper bound) of all
First_uncountable_ordinal
Axiom of set theory
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
Axiom_of_choice
Numerical ordering with a margin of error
In order theory, a branch of mathematics, a semiorder is a type of ordering for items with numerical scores, where items with widely differing scores are
Semiorder
Collection of mathematical objects
choice is equivalent with the fact that a well-order can be defined on every set, where a well-order is a total order such that every nonempty subset has a
Set_(mathematics)
American journalist and civil rights activist (1862–1931)
lynching as an instrument to maintain Southern order and discourage Black economic ventures. Ultimately, Wells concluded that appealing to reason and compassion
Ida_B._Wells
British order of chivalry established in 1896
The Royal Victorian Order (French: Ordre royal de Victoria) is a dynastic order of knighthood established in 1896 by Queen Victoria. It recognises distinguished
Royal_Victorian_Order
listing of Nigeria's 36 states ranked in order of their total population based on the 2006 census figures, as well as their 2020 projected populations, which
List of Nigerian states by population
List_of_Nigerian_states_by_population
Size of a possibly infinite set
classes of well-orderings of the natural numbers; each such well-ordering defines a countable ordinal, and ω 1 {\displaystyle \omega _{1}} is the order type
Cardinal_number
Number representing a continuous quantity
a least element in this ordering. (The standard ordering ≤ {\displaystyle \leq } of the real numbers is not a well-ordering since e.g. an open interval
Real_number
American actor and filmmaker (1915–1985)
George Orson Welles (May 6, 1915 – October 10, 1985) was an American actor and filmmaker. Remembered for his innovative work in film, radio, and theatre
Orson_Welles
Mathematical concept for comparing objects
relations are as ubiquitous in mathematics as order relations, the algebraic structure of equivalences is not as well known as that of orders. The former structure
Equivalence_relation
Heritage railway in North Norfolk, England
was authorised by the Wells and Walsingham Light Railway Order 1982, the terms of which were altered under the subsequent Wells and Walsingham Light Railway
Wells and Walsingham Light Railway
Wells_and_Walsingham_Light_Railway
Legal/criminal procedural television franchise
Law & Order is a media franchise composed of a number of related American television series created by Dick Wolf and produced by Wolf Entertainment. They
Law_&_Order_(franchise)
Catholic military order
Order of Knights of the Hospital of Saint John of Jerusalem, commonly known as the Knights Hospitaller (/ˈhɒspɪtələr/), is a Catholic military order.
Knights_Hospitaller
Type of binary relation
R relates a to b and b to c, then R also relates a to c. Every partial order and every equivalence relation is transitive. For example, less than and
Transitive_relation
Catholic military order, 1118 to 1312
speculative popular publications surrounding the order's early occupation of the Temple Mount in Jerusalem as well as speculation about what relics the Templars
Knights_Templar
Partially ordered set in which all subsets have both a supremum and infimum
lattices appear in many applications in mathematics and computer science. Both order theory and universal algebra study them as a special class of lattices.
Complete_lattice
In mathematics, invertible homomorphism
transitive, total, trichotomous, a partial order, total order, well-order, strict weak order, total preorder (weak order), an equivalence relation, or a relation
Isomorphism
Malicious manipulation of potable water resources
Well poisoning is the act of malicious manipulation of potable water resources in order to cause illness or death, or to deny an opponent access to fresh
Well_poisoning
Reversal of the order of elements of a binary relation
operation of complementation as well as with taking suprema and infima. Conversion is also compatible with the ordering of relations by inclusion. If a
Converse_relation
Character in the Law & Order TV series franchise
as well as in one episode of Homicide: Life on the Street. He also appeared in Exiled: A Law & Order Movie. Logan initially appeared on Law & Order from
Mike_Logan_(Law_&_Order)
finite. For trees over a well-ordered set, the Kleene–Brouwer order is itself a well-ordering if and only if the tree has no infinite branch. It is named
Kleene–Brouwer_order
Particular class of sets which can be described entirely in terms of simpler sets
{\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
Constructible_universe
of countable unions of scattered orders is a well-quasi-order. The order topology of a scattered order is scattered. The converse implication does not
Scattered_order
Special subset of a partially ordered set
filter or order filter is a special subset of a partially ordered set (poset), describing "large" or "eventual" elements. Filters appear in order and lattice
Filter_(mathematics)
in an episode in the next two seasons, as well as becoming a judge on the series' third spin-off, Law & Order: Trial by Jury. She appeared in the show's
List_of_Law_&_Order_episodes
Type of topology in mathematics
opposite convention also exists.) The following dictionary holds between order-theoretic notions and topological notions: Open sets are upper sets, Closed
Alexandrov_topology
Paradox in set theory
Russell–Myhill paradox The Burali-Forti paradox, about the order type of all well-orderings Curry's paradox (named after Haskell Curry), which does not
Russell's_paradox
Binary relation over a set and itself
endorelations include orders, graphs, and equivalences. Specialized studies of order theory and graph theory have developed understanding of endorelations. Terminology
Homogeneous_relation
Topics referred to by the same term
community Wells County (disambiguation) Wells Island, West Virginia Wells Township (disambiguation) Wells baronets, a member of the Order of Baronets
Wells
Conspiracy theory regarding a totalitarian world government
writer and futurist H. G. Wells went further than progressives in the 1940s, by appropriating and redefining the term "new world order" as a synonym for the
New World Order conspiracy theory
New_World_Order_conspiracy_theory
Nizari Isma'ili military order (1090–1256)
Order of Assassins (Arabic: حَشّاشُون, romanized: Ḥaššāšūn; Persian: حشاشين, romanized: Haššāšīn) was a Nizari Isma'ili Shia Islamic military order founded
Order_of_Assassins
Size of subsets in order theory
\delta } that is the order type of a cofinal subset of α . {\displaystyle \alpha .} The cofinality of a set of ordinals or any other well-ordered set is the
Cofinality
Visual depiction of a partially ordered set
In order theory, a Hasse diagram (/ˈhæsə/; German: [ˈhasə]) is a type of mathematical diagram used to represent a finite partially ordered set, in the
Hasse_diagram
Mathematical ordering with upper bounds
Join-semilattices (which are partially ordered sets) are directed sets as well, but not conversely. Likewise, lattices are directed sets both upward and
Directed_set
the order type of a well-ordering W is the set of all well-orderings which are similar to W. The set of ordinal numbers is the set of all order types
Implementation of mathematics in set theory
Implementation_of_mathematics_in_set_theory
Partially ordered vector space, ordered as a lattice
vector space or vector lattice is a partially ordered vector space where the order structure is a lattice. Riesz spaces are named after Frigyes Riesz who first
Riesz_space
Characterizes the height of any finite partially ordered set
of order theory and combinatorics, Mirsky's theorem characterizes the height of any finite partially ordered set in terms of a partition of the order into
Mirsky's_theorem
Computer markup language
1, 1 1 1)) ) Well-known binary (WKB) representations are typically shown in hexadecimal strings. The first byte indicates the byte order for the data:
Well-known text representation of geometry
Well-known_text_representation_of_geometry
English writer (1866–1946)
sceptical to Christianity, HG Wells had surprisingly positive views on Islam. He complimented how Islam brought equity and order to a tribalistic part of the
H._G._Wells
National shrine, chapel, well, and pilgrimage site in Flintshire
Well (Welsh: Ffynnon Wenffrewi) is a holy well and national shrine located in the town of Holywell in Flintshire, Wales. The patron saint of the well
St_Winefride's_Well
WELL ORDER
WELL ORDER
Male
English
Short form of English unisex Kelly, KELL means "bright-headed."
Boy/Male
Shakespearean
A Midsummer Night's Dream' Snout, a tinker, acts as Wall in the play within the play.
Boy/Male
Australian, British, English, Jamaican
Springs; From the Wells; From the Spring
Male
English
Short form of English William, WILL means "will-helmet."
Surname or Lastname
English
English : variant of Mill.German : variant of Melle.
Surname or Lastname
English
English : topographic name for someone who lived in a small valley, from Middle English, Old English dell ‘dell’, ‘valley’, or a habitational name from any of several minor places named Dell, from this word, for example in Buckinghamshire, Essex, and Sussex.German : from Low German delle ‘dell’, ‘depression’ (Middle High German telle ‘gorge’).
Surname or Lastname
English
English : habitational name from Ewell in Surrey or from Ewell Minnis or Temple Ewell in Kent, all named with Old English ǣwell ‘river source’.
Surname or Lastname
English
English : topographic name for someone who lived near a spring or stream, Middle English well(e) (Old English well(a)).German : from a short form of the personal names Wallo, Walilo.German : nickname from Middle High German wël ‘round’.
Female
English
Variant spelling of English Belle, BELL means "beautiful."Â
Surname or Lastname
Jewish (eastern Ashkenazic)
Jewish (eastern Ashkenazic) : nickname for a man with red hair, from Yiddish gel ‘red-headed’, Middle High German gel ‘yellow’, German gelb (see Geller).German : unexplained.English : from a short form of the personal name Julian.Variant of French Gille.
Surname or Lastname
English (chiefly northern)
English (chiefly northern) : topographic name for someone who lived by an area of high ground or by a prominent crag, from northern Middle English fell ‘high ground’, ‘rock’, ‘crag’ (Old Norse fjall, fell).English, German, and Jewish (Ashkenazic) : metonymic occupational name for a furrier, from Middle English fell, Middle High German vel, or German Fell or Yiddish fel, all of which mean ‘skin’, ‘hide’, or ‘pelt’. Yiddish fel refers to untanned hide, in contrast to pelts ‘tanned hide’ (see Pilcher).
Female
English
Pet form of English Eleanor, NELL means "foreign; the other."
Surname or Lastname
English
English : topographic name from Middle English wold ‘forest’ or ‘cleared upland’ (see Wald, Wold).Thomas Weld (1596–1661), born in Sudbury, Suffolk, England, was an influential Puritan divine who emigrated from Terling, Essex, to Roxbury, MA, in 1632.
Surname or Lastname
English
English : from the Middle English personal name Pell, a pet form of Peter.English : metonymic occupational name for a dealer in furs, from Middle English, Old French pel ‘skin’.English : variant of Pill 1.German : variant of Pelle or, in some instances, a variant of Pfell, the South German form of this name, from Middle High German phelle(e) ‘purple silk cloth’.
Boy/Male
German American Teutonic English
Will-helmet. Famous Bearers: poet and playwright William Shakespeare (1564-1616) and William...
Boy/Male
American, Australian, British, Chinese, Christian, English, French, German, Swedish, Teutonic
Purposeful Peace; Will-helmet; Will; Desire; Bright; Famous
Surname or Lastname
English
English : habitational name from any of several places named with the plural of Old English well(a) ‘spring’, ‘stream’, or a topopgraphical name from this word (in its plural form), for example Wells in Somerset or Wells-next-the-Sea in Norfolk.Translation of French Dupuis or any of its variants.One of numerous early immigrants from England bearing this name was Thomas Welles, governor of colonial CT, who was in Hartford, CT, by 1636.
Surname or Lastname
Scottish and northern English
Scottish and northern English : from the medieval personal name Will, a short form of William, or from some other medieval personal names with this first element, for example Wilbert or Willard.English : topographic name for someone who lived by a spring or stream, Middle English wille (from wiell(a), West Saxon form of Old English well(a) ‘spring’). The surname is found predominantly in the south and southwestern parts of the country.German : from a short form of any of the various Germanic personal names beginning with wil ‘will’, ‘desire’.
Surname or Lastname
English
English : topographic name for someone who lived by a stone-built wall, e.g. one used to fortify a town or to keep back the encroachment of the sea (Old English w(e)all, from Latin vallum ‘rampart’, ‘palisade’).Northern English : topographic name for someone who lived by a spring or stream, northern Middle English wall(e) (Old English (Mercian) wæll(a); compare Well).Irish : re-Anglicized form of de Bhál, a Gaelicized form of de Valle, the name of a Norman family established in Munster and Connacht.German : topographic name for someone who lived by a defensive wall, Middle High German wal.German : variant of Wahl 2.German : from a short form of the personal name Walther.Swedish : ornamental name from Swedish vall ‘grassy bank’, ‘pasture’, ‘grazing ground’, or in some cases a habitational name from a place named with this element.
Surname or Lastname
English
English : variant of Hill, from southeastern Middle English hell ‘hill’, a dialect form characteristic of Kent and Sussex.English : from a personal name, Helle, which may have been a variant of Elie (a Middle English form of Elias), or perhaps a short form of a personal name formed with Hild- as the first element (see Hilliard for example), or perhaps from the female personal name Helen.German : nickname from Middle High German hell ‘bright’, ‘shining’.German : variant of Helle 3.
WELL ORDER
WELL ORDER
WELL ORDER
WELL ORDER
WELL ORDER
WELL ORDER
WELL ORDER
a.
Good in condition or circumstances; desirable, either in a natural or moral sense; fortunate; convenient; advantageous; happy; as, it is well for the country that the crops did not fail; it is well that the mistake was discovered.
a.
Being in health; sound in body; not ailing, diseased, or sick; healthy; as, a well man; the patient is perfectly well.
v. t. & i.
See 2d Will.
v. t.
To put a bell upon; as, to bell the cat.
v. t.
To inclose with a wall, or as with a wall.
n.
One who wishes well, or means kindly.
v. t.
To make bell-mouthed; as, to bell a tube.
a. & adv.
Well.
v. t.
To furnish with a welt; to sew or fasten a welt on; as, to welt a boot or a shoe; to welt a sleeve.
n.
Prosperity; happiness; well-being; weal.
v. t.
To pour forth, as from a well.
a.
Being well folded.
n.
A cell; a house.
a.
Speaking well; speaking with fitness or grace; speaking kindly.
a.
Spoken with propriety; as, well-spoken words.
v. t. & i.
See 2d Will.
n.
The state or condition of being well; welfare; happiness; prosperity; as, virtue is essential to the well-being of men or of society.
a.
Well put together; having symmetry of parts.
a.
Safe; as, a chip warranted well at a certain day and place.
a.
Polite; well-bred; complaisant; courteous.