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Operators to indicate precedence order
mathematical notation, ordered set operators indicate whether an object precedes or succeeds another. These relationship operators are denoted by the unicode
Ordered_set_operators
Mathematical operator
families". A set together with a closure operator on it is sometimes called a closure space. Closure operators are also called "hull operators", which prevents
Closure_operator
in fuzzy logic, the ordered weighted averaging (OWA) operators provide a parameterized class of mean type aggregation operators. They were introduced
Ordered_weighted_averaging
2018 American film
building and meet one night when their bosses need dinner. Harper has ordered dinner for Kirsten but has no cash to pay for it; Charlie, who was not
Set_It_Up
Order-preserving mathematical function
mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose
Monotonic_function
Identities and relationships involving sets
relations. Any set of sets closed under the set-theoretic operations forms a Boolean algebra with the join operator being union, the meet operator being intersection
Algebra_of_sets
Number representing a continuous quantity
real associative algebra. Positive-definite operators correspond to the positive reals and normal operators correspond to the complex numbers. Mathematics
Real_number
Set whose pairs have minima and maxima
subdisciplines of order theory and abstract algebra. It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a
Lattice_(order)
Branch of mathematics
then a ≤ c (transitivity). A set with a partial order on it is called a partially ordered set, poset, or just ordered set if the intended meaning is clear
Order_theory
Function acting on function spaces
built from them are called differential operators, integral operators or integro-differential operators. Operator is also used for denoting the symbol of
Operator_(mathematics)
Subset of a preorder that contains all larger elements
In mathematics, an upper set S {\displaystyle S} of a partially ordered set X {\displaystyle X} is a subset such that if s is in S and if x in X is larger
Upper_and_lower_sets
Operation on the subsets of a set
a set form a partially ordered set (poset) for inclusion. Closure operators allow generalizing the concept of closure to any partially ordered set. Given
Closure_(mathematics)
Abstraction of linear independence of vectors
independent sets; bases or circuits; rank functions; closure operators; and closed sets or flats. In the language of partially ordered sets, a finite simple
Matroid
Generalization of "n-th" to infinite cases
least two types higher than elements of the original well-ordered set, so type-raising operators may be required to "label" the original elements with them
Ordinal_number
Relationship between elements of two sets
relation over sets X {\displaystyle X} and Y {\displaystyle Y} is a set of ordered pairs ( x , y ) {\displaystyle (x,y)} , where x {\displaystyle x} is
Binary_relation
Set with operations obeying given axioms
structure. Vertex operator algebra Von Neumann algebra: a *-algebra of operators on a Hilbert space equipped with the weak operator topology. Algebraic
Algebraic_structure
Non-perturbative approach to quantum field theory
by operators. To know the result of making two physical observations at two points z {\displaystyle z} and w {\displaystyle w} , their operators can
Operator_product_expansion
Mathematical set formed from two given sets
mathematics, specifically set theory, the Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is an
Cartesian_product
Topics referred to by the same term
music videos by Miki Nakatani, 1998 Complete set of commuting operators (or CSCO), a set of commuting operators in quantum mechanics whose eigenvalues are
Completeness
Programming language construct
well ordered. The most common numerical relational operators used in programming languages are shown below. Standard SQL uses the same operators as BASIC
Relational_operator
Twin-engine light utility helicopter
the Polish Air Force. Australia Operators: Royal Flying Doctor Service WA Police SA Police Brazil Brazilian operators: Bahia State Public Security Maranhão
Eurocopter_EC145
Method of construction of the real numbers
the rational numbers to any totally ordered set by defining a Dedekind cut as a partition of a totally ordered set into two non-empty parts A and B, such
Dedekind_cut
Performing order of mathematical operations
than 16/(4/4) = 16; such operators are referred to as "left associative". Exceptions exist; for example, languages with operators corresponding to the cons
Order_of_operations
Greatest lower bound and least upper bound
(abbreviated inf; pl.: infima) of a subset S {\displaystyle S} of a partially ordered set P {\displaystyle P} is the greatest element in P {\displaystyle P} that
Infimum_and_supremum
Branch of mathematics that studies sets
the validity of inferences in term logic). Set theory is used to introduce students to logical operators (NOT, AND, OR), and semantic or rule description
Set_theory
Term in the mathematical area of order theory
greatest lower bounds (infima, ∧) Upper sets and lower sets Ideals and filters Closure operators and kernel operators. Examples of notions which are self-dual
Duality_(order_theory)
Bound lattice in which every element has a complement
from the calculus of linear subspaces [of a Hilbert space] with respect to set products, linear sums and orthogonal complements" corresponding to the roles
Complemented_lattice
Mathematical set containing no elements
for the maximum and supremum operators, while positive infinity is the identity element for the minimum and infimum operators. In any topological space X
Empty_set
Type of topology in mathematics
path connected. Considering the interior operator and closure operator to be modal operators on the power set Boolean algebra of an Alexandroff-discrete
Alexandrov_topology
Symbol connecting formulas in logic
interpretation. These symbols are called logical connectives, logical operators, propositional operators, or, in classical logic, truth-functional connectives. For
Logical_connective
universal set, as in definition 2. × (multiplication sign) See also × in § Arithmetic operators. 1. Denotes the Cartesian product of two sets. That is
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Online gambling service provider
Philippine offshore gaming operators (POGOs), renamed Internet gaming licensees (IGLs) in October 2023, are firms operating in the Philippines that offer
Philippine offshore gaming operator
Philippine_offshore_gaming_operator
Use of coordinates for representing vectors
^{n}} can also be specified as a row or column matrix containing the ordered set of components. A vector specified as a row matrix is known as a row vector;
Vector_notation
Paris Metro train
(French: Métro Pneu appel d'offres de 2014; English: Rubber-tyred metro ordered in 2014) is a rubber-tyred electric multiple unit for the Paris Metro.
MP_14_(Paris_Metro)
Multi-role combat aircraft family by Dassault
delivered on 29 January 2025. Future operators Serbia Serbian Air Force and Air Defence – 12 aircraft (F4 version) ordered in 2024 with deliveries to be completed
Dassault_Rafale
Particular correspondence between two partially ordered sets
connection is a particular correspondence (typically) between two partially ordered sets (posets). Galois connections find applications in various mathematical
Galois_connection
Partially ordered vector space, ordered as a lattice
In mathematics, a Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice
Riesz_space
2010s narrow-body airliner by Airbus
There are 1,752 A321neo aircraft in service with 88 operators as of June 2025. The five largest operators are Wizz Air (156), IndiGo (143), American Airlines
Airbus_A321neo
List of military aircraft users
the Pakistan Air Force (PAF), a major non-NATO US ally, are the primary operators of the aircraft. With the evolution of sales under Foreign Military Sales
General Dynamics F-16 Fighting Falcon operators
General_Dynamics_F-16_Fighting_Falcon_operators
British gambling company
verification] In the summer of 2019, the largest UK bookmakers and online casino operators William Hill, GVC Holdings, Flutter Entertainment, Stars Group and bet365
Bet365
Partially ordered set in which all subsets have both a supremum and infimum
In mathematics, a complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). A conditionally
Complete_lattice
Set of aggregation operators that generalise the Yager's OWA
Type-1 OWA operators are a set of aggregation operators that generalise the Yager's OWA (ordered weighted averaging) operators in the interest of aggregating
Type-1_OWA_operators
Public transport operator in Melbourne, Australia
Transport who leases it to transport operators such as Metro as well as entering into franchise agreements with the operators for them to run public transport
Metro_Trains_Melbourne
Family of electric passenger trains
Aventra came from the Crossrail programme in 2014. Numerous other operators have since ordered the type, including London Overground, Greater Anglia, South
Alstom_Aventra
General concept and operation in mathematics
analogous duality of ∀ and ∃. Other dual modal operators behave similarly. For example, temporal logic has operators denoting "will be true at some time in the
Duality_(mathematics)
Class of electric trains operating in Sydney, Australia
2019, all the 24 B sets were delivered and had replaced the 48 remaining S sets. In February 2019, a further 17 B sets were ordered, with the first two
New_South_Wales_A_and_B_sets
Sets whose elements have degrees of membership
family of fuzzy sets recursively. It is noteworthy that the generally accepted standard operators for the union and intersection of fuzzy sets are the max
Fuzzy_set
Association of one output to each input
codomain. Mathematically, a binary relation between two sets X and Y is a subset of the set of all ordered pairs ( x , y ) {\displaystyle (x,y)} such that x
Function_(mathematics)
lists active operators of the aircraft. List of Boeing 777 orders and deliveries List of Boeing 747 operators List of Airbus A350 operators List of Airbus
List_of_Boeing_777_operators
Topological complex vector space
linear operators on a complex Hilbert space with two additional properties: A is a topologically closed set in the norm topology of operators. A is closed
C*-algebra
partially ordered sets, a pseudoideal is a subset characterized by a bounding operator LU. LU(A) is the set of all lower bounds of the set of all upper
Pseudoideal
In geometry, set whose intersection with every line is a single line segment
sets form a chain (a totally ordered set) under inclusion. For this property, the restriction to chains is important, as the union of two convex sets
Convex_set
Pair of logical equivalences
Morgan's laws commonly apply to text searching using Boolean operators AND, OR, and NOT. Consider a set of documents containing the words "cats" and "dogs". De
De_Morgan's_laws
Programming language family
"1 + 2 + 3 + 4". Lisp has no notion of operators as implemented in ALGOL-derived languages. Arithmetic operators in Lisp are variadic functions (or n-ary)
Lisp_(programming_language)
Algebraic concept in measure theory, also referred to as an algebra of sets
can be generalized to fields of sets on arbitrary algebraic structures having both operators and relations as operators can be viewed as a special case
Field_of_sets
Number in {..., –2, –1, 0, 1, 2, ...}
theorem of arithmetic. Z {\displaystyle \mathbb {Z} } is a totally ordered set without upper or lower bound. The ordering of Z {\displaystyle \mathbb
Integer
Algebra used in 2D conformal field theories and string theory
Physically, the vertex operators arising from holomorphic field insertions at points in two-dimensional conformal field theory admit operator product expansions
Vertex_operator_algebra
*-algebra of bounded operators on a Hilbert space
algebra generated by a set of bounded operators on a Hilbert space is the smallest von Neumann algebra containing all those operators. The tensor product
Von_Neumann_algebra
Military training aircraft
Force 6 T-346A ordered in June 2009 3 T-346A ordered in December 2014 9 T-346A ordered in March 2016, all delivered by February 2018 20 ordered in December
Alenia_Aermacchi_M-346_Master
Diesel multiple unit train
toured the US Between 2002–2004 to demonstrate the DMU to potential future operators. In 2005, the first bi-level DMU would be built for Tri Rail as part of
Colorado_Railcar_DMU
Franchised bus network in West Yorkshire, England
2025, nineteen different bus operators run public bus services in West Yorkshire, with the three largest bus operators in the county being First West
Weaver_Network
Multi-national four-engine turboprop military transport aircraft
their support for the project. A total of 174 A400M aircraft had been ordered by eight nations by July 2011. In March 2013, the A400M received European
Airbus_A400M_Atlas
Glossary of terms used in branch of mathematics
chain is a totally ordered set or a totally ordered subset of a poset. See also total order. Chain complete. A partially ordered set in which every chain
Glossary_of_order_theory
Functional analysis concept
can sometimes be extended to compact operators using similar arguments. By contrast, the study of general operators on infinite-dimensional spaces often
Compact operator on Hilbert space
Compact_operator_on_Hilbert_space
Bus operator in South-East England
after routes 353 and 354 were re-timetabled.[citation needed] Two coach operators, Southlands Travel of Bromley and RB Coaches, were taken over by Metrobus
Metrobus_(South_East_England)
Algebraic manipulation of "true" and "false"
the corresponding binary operators AND ( ∧ {\displaystyle \land } ) and OR ( ∨ {\displaystyle \lor } ) and the unary operator NOT ( ¬ {\displaystyle \neg
Boolean_algebra
Expectation value of time-ordered quantum operators
Green's functions, are vacuum expectation values of time-ordered products of field operators. They are a key object of study in quantum field theory where
Correlation function (quantum field theory)
Correlation_function_(quantum_field_theory)
Set of rules defining correctly structured programs
in Python 3. The binary comparison operators such as == and > return either True or False. The Boolean operators and and or use minimal evaluation. For
Python_syntax_and_semantics
Re-engined version of the A320 family
aircraft are in service with 127 operators, 85 of which use CFM engines, and 42 PW engines. The five largest operators are IndiGo operating 353, Wizz Air
Airbus_A320neo_family
Medium tank/Main battle tank
were ordered in 1963 from the Soviet Union and delivered in 1963 (the vehicles were previously in Soviet service). 25 T-54s and 25 T-55s were ordered in
T-54/T-55 operators and variants
T-54/T-55_operators_and_variants
European tactical military transport aircraft
become the 39th operator of the C-295 aircraft worldwide and the eighth in the Asia-Pacific region. A total of four aircraft have been ordered and the first
Airbus_C295
Soviet senior nuclear engineer (1960–1986)
shutdown as operator. The operators attempted to perform a rundown test before scheduled routine maintenance. In preparation, Anatoly Dyatlov ordered the power
Leonid_Toptunov
Type of vector space in math
integral equations. Fredholm operators are bounded operators that are invertible modulo compact operators. Thus an operator T {\displaystyle T} is Fredholm
Hilbert_space
Airline of Angola
marked the first time Heli Malongo had ordered Sikorsky helicopters. The airline made the purchase in order to set up Angola's first search and rescue service
Heli_Malongo_Airways
Set of elements in any of some sets
In set theory, the union (denoted by ∪) of a collection of sets is the set of all elements in the collection. It is one of the fundamental operations
Union_(set_theory)
Generalization of the real numbers
such, they form an ordered field. If formulated in von Neumann–Bernays–Gödel set theory, the surreal numbers are a universal ordered field in the sense
Surreal_number
Main battle tank
service as of 2025. 50 bought from Yemen and 171 T-72UA1 vehicles reportedly ordered from Ukraine in 2011. Georgia –140 T-72B/B1/SIM1 in service as of 2025
T-72_operators_and_variants
Number used for counting
themselves are labeled using a well-ordered set; every element always has a clear next element. Every well-ordered set has an order type, which is the ordinal
Natural_number
Mathematical exercise
and related areas of mathematics, the set of all possible topologies on a given set forms a partially ordered set. This order relation can be used for
Comparison_of_topologies
Twin-engined, medium-lift helicopter manufactured by Leonardo
obtained by operators such as CHC Helicopter, Gulf Helicopters, and Weststar Aviation. Its performance has made it popular amongst operators supporting
AgustaWestland_AW139
requires all DTH operators in India to only use satellites commissioned by the Indian Space Research Organisation (ISRO). DTH operators may use capacity
Direct-to-home television in India
Direct-to-home_television_in_India
extreme value and mathematical optimization. Partially ordered set Preorder Totally ordered set Total preorder Chain Trichotomy Extended real number line
List_of_order_theory_topics
Executive trijet aircraft by Dassault
S. coasts. Corporate and charter operators use their Falcon 8Xs 600 to 850 hours per year, while individual operators fly theirs 300 to 400 hours per year
Dassault_Falcon_7X
American tandem-rotor helicopter introduced in 1962 during the Cold War
version of the Chinook is the Boeing Vertol 234. It has been used by civil operators not only for passenger and cargo transport, but also for aerial firefighting
Boeing_CH-47_Chinook
Single-level passenger railcar model
in 2026, followed by Northeast Regional sets in 2027. Illinois, Michigan, Missouri, and Wisconsin have ordered 97 Venture cars for the Amtrak Midwest routes
Siemens_Venture
Swiss built multiple unit passenger trainset
from operators across 24 countries. The first bi-mode FLIRT units, combining overhead electric operation with diesel power packs, were ordered by Italy's
Stadler_FLIRT
Concept in functional analysis
ISBN 978-1-4612-7155-0. OCLC 840278135. Positive linear operators and approximation properties A Class Of Positive Linear Operators And Applications To Nonlinear Boundary
Positive_linear_operator
Family of transport aircraft by CASA and IPTN
74 had been placed by military operators while 59 were attributed to civil operators; of these, 85 had been ordered by Indonesian customers while 22
CASA/IPTN_CN-235
Branch of elementary mathematics
} {\displaystyle 3=2\cup \{2\}=\{0,1,2\}} . Integers can be defined as ordered pairs of natural numbers where the second number is subtracted from the
Arithmetic
2025 aviation accident in India
been properly set for take-off at five degrees. The report did not identify any mechanical faults nor recommend safety actions for operators or manufacturers
Air_India_Flight_171
Mathematical operation
} For a given set V , {\displaystyle V,} the collection of all binary relations on V {\displaystyle V} forms a Boolean lattice ordered by inclusion (
Composition_of_relations
Chinese battery electric single-decker bus
planned to be operated across the country. 100 Yutong E12s were ordered for bus operators in Santiago de Chile in 2018, as part of a scheme seeking to electrify
Yutong_E10
American spy thriller television series
airing on Paramount+ with Showtime on June 27. CIA officer "Martian" is ordered to abandon his undercover life and return to London Station. A past love
The_Agency_(2024_TV_series)
Wide-body jet airliner developed from A330
economy) There are 195 aircraft in service with 25 operators as of May 2026[update]. The five largest operators of A330neo are Delta Air Lines (39), TAP Air
Airbus_A330neo
Array data structure that compactly stores bits
usual bitwise operators (~ | & ^), and individual bits can be tested and set using the vec function. In Ruby, one can access (but not set) a bit of an
Bit_array
Set of rules defining correctly structured programs
names when discussing functions and operators (for example, "product" for ×/) but the core functions and operators provided by the language are denoted
APL_syntax_and_symbols
Linear operator related to topological vector spaces
nuclear operators are an important class of linear operators introduced by Alexander Grothendieck in his doctoral dissertation. Nuclear operators are intimately
Nuclear_operator
{\displaystyle R} on a set X {\displaystyle X} is the smallest reflexive relation on X {\displaystyle X} that contains R {\displaystyle R} , i.e. the set R ∪ { ( x
Reflexive_closure
Type of mathematical space
subcover. It is complete but not totally bounded. For an ordered space (X, <) (i.e. a totally ordered set equipped with the order topology), the following are
Compact_space
Class of cruise ships under construction for MSC Cruises
the ships. The World-class design would become the third new prototype ordered by MSC in recent years, following its commitments to the Meraviglia and
World-class_cruise_ship
ORDERED SET-OPERATORS
ORDERED SET-OPERATORS
Female
Egyptian
, the mother of Fai-hor-ou-oer.
Male
Hebrew
Variant spelling of Hebrew Sheth, SHET means "buttocks."
Boy/Male
Indian
Responsibility; Ordered
Male
Hindi/Indian
(सेठ) Hindi name derived from the Sanskrit word setu, SETH means "bridge." Compare with other forms of Seth.
Female
Egyptian
, an uncertain goddess.
Boy/Male
English Arthurian Legend
Brave.
Boy/Male
American, British, Christian, English
Brave; Brave Counselor
Surname or Lastname
English (Lancashire)
English (Lancashire) : habitational name from a place in Lancashire, called Ormerod, from the Old Norse personal name Ormr (see Orme 1) or Ormarr (a compound of orm ‘serpent’ + herr ‘army’) + Old English rod ‘clearing’.
Female
Egyptian
, a sister of Sekherta.
Male
English
Anglicized form of Hebrew Sheth, SETH means "buttocks." In the bible, this is the name of the third son of Adam and Eve. Compare with other forms of Seth.
Female
English
Short form of English Elizabeth, BET means "God is my oath."Â
Boy/Male
Arabic, Australian, Muslim
Ordered; Appointed
Male
English
Short form of English Stephen, STE means "crown."
Female
Egyptian
, the wife of Osirtesen.
Boy/Male
Egyptian Hebrew Swedish
Son of Seb and Nut.
Male
English
Old English Arthurian legend name of a Knight of the Round Table who was the illegitimate son and traitor of King Arthur, possibly MORDRED means "sea counsel." He was brother (or half-brother) to Agravain, Gaheris, Gareth, and Gawain, and noted for having crowned himself and married Guinevere while Arthur was waging war on Emperor Lucius of Rome. He was killed by Arthur at the Battle of Camlann.Â
Female
Egyptian
, a sister of Sekherta.
Female
Egyptian
, a wife and daughter of Antef.
Surname or Lastname
English
English : variant spelling of See.
Female
Egyptian
, second wife of Antef.
ORDERED SET-OPERATORS
ORDERED SET-OPERATORS
Boy/Male
Arabic, Australian
Stars
Boy/Male
Australian, Norse, Scandinavian
God of Destruction; Trickster God; Break
Boy/Male
Muslim
Desire, Wish
Surname or Lastname
English
English : habitational name from Lingart, Lancashire, or Lingards Wood in Marsden, West Yorkshire, both named from Old English līn ‘flax’ + garðr ‘enclosure’.
Female
English
Spanish equivalent of English Alice, ALICIA means "noble sort."
Girl/Female
Tamil
Trishona | தà¯à®°à®¿à®·à¯‹à®¨à®¾
Desire
Boy/Male
Sikh
One colored in the union of God
Boy/Male
Arabic, Australian, German, Turkish
Leader
Girl/Female
Hindu, Indian
Queen
Surname or Lastname
Americanized form of French Petitjean.English
Americanized form of French Petitjean.English : variant spelling of Pettyjohn.
ORDERED SET-OPERATORS
ORDERED SET-OPERATORS
ORDERED SET-OPERATORS
ORDERED SET-OPERATORS
ORDERED SET-OPERATORS
n.
One who puts in order, arranges, methodizes, or regulates.
n.
One who gives orders.
v. t.
To cause to sit; to make to assume a specified position or attitude; to give site or place to; to place; to put; to fix; as, to set a house on a stone foundation; to set a book on a shelf; to set a dish on a table; to set a chest or trunk on its bottom or on end.
v. i.
To fit or suit one; to sit; as, the coat sets well.
a.
Being on duty; keeping order; conveying orders.
v. t.
To compose; to arrange in words, lines, etc.; as, to set type; to set a page.
n.
That which is set, placed, or fixed.
a.
Set with briers.
a.
Fixed in position; immovable; rigid; as, a set line; a set countenance.
a.
Observant of order, authority, or rule; hence, obedient; quiet; peaceable; not unruly; as, orderly children; an orderly community.
a.
Covered or adorned with osiers; as, osiered banks.
a.
Well-ordered; orderly; regular; methodical.
a.
Conformed to order; in order; regular; as, an orderly course or plan.
imp. & p. p.
of Order
n.
See Set, n., 2 (e) and 3.
imp. & p. p.
of Set
adv.
According to due order; regularly; methodically; duly.
v. t.
To put in order in a particular manner; to prepare; as, to set (that is, to hone) a razor; to set a saw.
a.
Regular; uniform; formal; as, a set discourse; a set battle.
a.
Established; prescribed; as, set forms of prayer.