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Special case of discrete optimization
In discrete optimization, a special ordered set (SOS) is an ordered set of variables used as an additional way to specify integrality conditions in an
Special_ordered_set
Mathematical set with an ordering
transitive. A partially ordered set (poset for short) is an ordered pair P = ( X , ≤ ) {\displaystyle P=(X,\leq )} consisting of a set X {\displaystyle X}
Partially_ordered_set
Class of mathematical orderings
well order, well ordered, and well ordering. Every non-empty well-ordered set has a least element. Every element s of a well-ordered set, except a possible
Well-order
Generalised alphabetical order
order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations
Lexicographic_order
Well-quasi-ordering of finite trees
Kruskal's tree theorem states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic embedding. A
Kruskal's_tree_theorem
Special subset of a partially ordered set
In mathematics, a filter or order filter is a special subset of a partially ordered set (poset), describing "large" or "eventual" elements. Filters appear
Filter_(mathematics)
Branch of mathematics
applications. Driven by the wide practical usage of orders, numerous special kinds of ordered sets have been defined, some of which have grown into mathematical
Order_theory
Number representing a continuous quantity
largest ordered set that is complete and locally Archimedean. As with the previous two examples, this set is no longer a field or additive group. Ordered fields
Real_number
Isomorphism type of ordered sets
In mathematics, especially in set theory and order theory, two ordered sets X and Y are said to have the same order type if they are order isomorphic
Order_type
Alternative mathematical ordering
requirement results in a partial cyclic order. A set with a cyclic order is called a cyclically ordered set or simply a cycle.[nb] Some familiar cycles are
Cyclic_order
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
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
2026 Marvel Studios television special
that the special was in development under the "Special Presentation" banner in February 2025. Reinaldo Marcus Green was set to direct the special and was
The_Punisher:_One_Last_Kill
Algebraic object with an ordered structure
orderings. Every subfield of an ordered field is also an ordered field in the inherited order. Every ordered field contains an ordered subfield that is isomorphic
Ordered_field
Generalization of "n-th" to infinite cases
extend this process to various infinite sets, ordinal numbers are defined more generally as a linearly ordered class of numbers that include the natural
Ordinal_number
Partially ordered set in which all subsets have both a supremum and infimum
special class of lattices. Complete lattices must not be confused with complete partial orders (CPOs), a more general class of partially ordered sets
Complete_lattice
On chains and antichains in partial orders
combinatorics, Dilworth's theorem states that, in any finite partially ordered set, the maximum size of an antichain of incomparable elements equals the
Dilworth's_theorem
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
Mathematical result or axiom on order relations
partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset, where "maximal" is with respect to set inclusion
Hausdorff_maximal_principle
there are 126 card sets for the game released in English and as of April 2022, there are 91 released in Japan, including special sets. As of September 2017
List of Pokémon Trading Card Game sets
List_of_Pokémon_Trading_Card_Game_sets
Vector space with a partial order
In mathematics, an ordered vector space or partially ordered vector space is a real vector space equipped with a partial order that is compatible with
Ordered_vector_space
Topics referred to by the same term
SOS2 may refer to: Son of Sevenless, a set of encoding genes Special ordered set of type 2, a structure in discrete optimization This disambiguation page
SOS2
Collection of mathematical objects
and the negation is the set complement. As for every Boolean algebra, the powerset is also a partially ordered set for set inclusion. It is also a complete
Set_(mathematics)
Freedom limited by the need for social order
contended the Constitution's original intent is a framework for ordered liberty, not a fixed set of rules. It highlights the founders' use of historical lessons
Ordered_liberty
In mathematics, especially order theory, a prefix ordered set generalizes the intuitive concept of a tree by introducing the possibility of continuous
Prefix_order
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)
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)
Existence of certain infima or suprema of a given poset
suprema of a given partially ordered set (poset). The most familiar example is the completeness of the real numbers. A special use of the term refers to
Completeness_(order_theory)
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
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)
Special type of lattice
of intuitionistic logic, which makes them a special case of the first example. Every totally ordered set is a distributive lattice with max as join and
Distributive_lattice
Season of American television series
crime-drama television series Law & Order: Special Victims Unit was ordered on February 27, 2020, by NBC. Set to air during the 2020–2021 television season
Law & Order: Special Victims Unit season 22
Law_&_Order:_Special_Victims_Unit_season_22
Military unit of the Indian Army
The Para (Special Forces), informally referred to as Para SF, is a group of special forces battalions of the Parachute Regiment in the Indian Army. These
Para_(Special_Forces)
Type of binary relation
The set N × N of pairs of natural numbers, ordered by (n1, n2) < (m1, m2) if and only if n1 < m1 and n2 < m2. Every class whose elements are sets, with
Well-founded_relation
Topics referred to by the same term
process Son of sysreport, in Linux; see Red Hat § Utilities and tools Special ordered set, in optimization Structural operational semantics, in computer programming
SOS_(disambiguation)
British Ministry of Defence directorate
Special Forces (UKSF) is a directorate comprising the Special Air Service, the Special Boat Service, the Special Reconnaissance Regiment, the Special
United_Kingdom_Special_Forces
Non-empty family of sets that is closed under finite unions and subsets
partially ordered set (an ideal on a set X {\displaystyle X} is an ideal on the powerset P ( X ) {\displaystyle {\mathcal {P}}(X)} partially ordered by inclusion)
Ideal_on_a_set
Season of American television series
crime-drama television series Law & Order: Special Victims Unit was ordered on February 27, 2020, by NBC. It was set to air during the 2021–2022 television
Law & Order: Special Victims Unit season 23
Law_&_Order:_Special_Victims_Unit_season_23
Term in the mathematical area of order theory
mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted by Pop or Pd. This
Duality_(order_theory)
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
Sets whose elements have degrees of membership
[0, 1]. Fuzzy sets generalize classical sets, since the indicator functions (aka characteristic functions) of classical sets are special cases of the membership
Fuzzy_set
Set theory concept
{\mathcal {F}}\,} must include all club sets. Clubsuit Filter (mathematics) – Special subset of a partially ordered set Filters in topology – Use of filters
Club_set
Season of television series
Vaughn (Hunter Schafer) speaks to a therapist. In October 2020, HBO ordered two specials to "bridge the gap" between season 1 and season 2, production of
Euphoria_specials
Relationship between two sets, defined by a set of ordered pairs
relation or they are not. Formally, a relation R over a set X can be seen as a set of ordered pairs (x,y) of members of X. The relation R holds between
Relation_(mathematics)
Type of monotone function
mathematics, an order embedding is a special kind of monotone function, which provides a way to include one partially ordered set into another. Like Galois connections
Order_embedding
U.S. Navy's special operations force
small-unit special operation missions in maritime, jungle, urban, arctic, mountainous, and desert environments. SEALs are typically ordered to capture
United_States_Navy_SEALs
Tree in set theory
(Schlindwein 1994). A special Aronszajn tree can be constructed as follows. The elements of the tree are certain well-ordered sets of rational numbers with
Aronszajn_tree
companies) in the battlefield. Germany has ordered 353 platoon systems, meaning about 12000 individual sets, of IdZ-ES (ES Enhanced System) from Rheinmetall
List of modern equipment of the German Army
List_of_modern_equipment_of_the_German_Army
Maximal proper filter
mathematical field of order theory, an ultrafilter on a given partially ordered set (or "poset") P {\textstyle P} is a certain subset of P , {\displaystyle
Ultrafilter
General concept and operation in mathematics
of Galois theory. Given a poset P = (X, ≤) (short for partially ordered set; i.e., a set that has a notion of ordering but in which two elements cannot
Duality_(mathematics)
Collection of porcelain in Lincoln's White House
set of much plainer buff-banded china was ordered in the Lincoln administration, and was used for family non-state entertaining. Mrs. Lincoln ordered
China service of the Lincoln administration
China_service_of_the_Lincoln_administration
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
American animated sitcom
Adventures and features college versions of the characters. Two seasons were ordered to be produced by Amblin Television and Warner Bros. Animation. The first
Tiny_Toons_Looniversity
President of the United States from 2009 to 2017
making extensive use of special forces, while encouraging greater reliance on host-government militaries. Obama also ordered the 2011 military intervention
Barack_Obama
Type of topology in mathematics
be modal operators on the power set Boolean algebra of an Alexandroff-discrete space, their construction is a special case of the construction of a modal
Alexandrov_topology
2023 American reality television series
On September 7, 2022, it was announced that Fox had ordered the series, originally titled Special Forces: The Ultimate Test, with Sophie Leonard, Alicia
Special Forces: World's Toughest Test
Special_Forces:_World's_Toughest_Test
US state elections
of Arkansas Sarah Huckabee Sanders ordered the special elections to be moved to March after court orders. A special election was made necessary in Senate
2026 Arkansas state legislative special elections
2026_Arkansas_state_legislative_special_elections
Reflexive and transitive binary relation
q} . The partially ordered set ( X / ⇔ , ⇐ ) {\displaystyle \left(X/\Leftrightarrow ,\Leftarrow \right)} is hence also a directed set. See Lindenbaum–Tarski
Preorder
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
Size of a set in mathematics
well-ordered set is isomorphic to a unique ordinal number, called the order type of the set. By the well-ordering theorem, every set can be well-ordered.
Cardinality
Mathematical set of all subsets of a set
elements in the set S or |S| = n. First, the enumerated set { (x, 1), (y, 2), (z, 3) } is defined in which the number in each ordered pair represents
Power_set
American TV series or program
Keith David ordered at Adult Swim". EW.com. Retrieved July 28, 2025. "Rick and Morty Spin-off TV Show With Surprising Character Trailer Sets Release Date"
President_Curtis_(TV_series)
Relation between pairs of arithmetic functions
arbitrary locally finite partially ordered set, with Möbius' classical formula applying to the set of the natural numbers ordered by divisibility: see incidence
Möbius_inversion_formula
Equivalence of partially ordered sets
order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets (posets). Whenever two
Order_isomorphism
Multi-course restaurant menu at fixed price
may be called prix fixe ([pʁi fiks], lit. 'fixed price'). The terms set meal and set menu are also used. Table d'hôte contrasts with à la carte, where customers
Table_d'hôte
was captured in January 1943 in the Gabès area of Tunisia by a special anti-SAS unit set up by the Germans.[better source needed] Stirling escaped and
History of the Special Air Service
History_of_the_Special_Air_Service
Set of the elements not in a given subset
In set theory, the complement of a set A, often denoted by A c {\displaystyle A^{c}} (or A′), is the set of elements not in A. When all elements in the
Complement_(set_theory)
The Animated Series Volume One set, episodes 29 to 56 in the Volume Two set, and episodes 57 to 85 in the Volume Three set. Due to the show's success, the
List of Batman: The Animated Series episodes
List_of_Batman:_The_Animated_Series_episodes
Standard for language representation
standard codes in Sets 1 and 2 (where the special code mis is not suitable), or a three-letter code for collections like standard codes in Set 5. Types (for
ISO_639
Characters for drawing frames and boxes
proprietary character sets, usually extensions to ISO 8859 character sets, which include box-drawing characters or other special symbols. Other types of
Box-drawing_characters
A type of item in a relational database, in computing
as the product number (foreign key) that was ordered, the quantity, the price, any discount, any special options, and so on. There may be zero, one or
Weak_entity
2002 video game
specifically for the game. A soundtrack CD, Jet Set Radio Future Music Sampler, was given to people who pre-ordered the game in the United States, featuring
Jet_Set_Radio_Future
Season of American television series
of the American crime-drama television series Law & Order: Special Victims Unit was ordered on February 27, 2020, by NBC, which premiered on September
Law & Order: Special Victims Unit season 24
Law_&_Order:_Special_Victims_Unit_season_24
Axiom of set theory
a set. So no contradiction to regularity can be proved. The axiom of regularity enables defining the ordered pair (a,b) as {a,{a,b}}; see ordered pair
Axiom_of_regularity
American television series (1999–present)
Law & Order: Special Victims Unit (often shortened to Law & Order: SVU or SVU) is an American police procedural crime drama television series created
Law & Order: Special Victims Unit
Law_&_Order:_Special_Victims_Unit
Covert and paramilitary unit of the CIA
The Special Activities Center (SAC) is the center of the United States Central Intelligence Agency (CIA) responsible for covert operations. The clandestine
Special_Activities_Center
American television series (2018–present)
spin-off had been ordered to series. On July 8, 2021, it was reported that Luke Kleintank, Heida Reed and Vinessa Vidotto were set to casts in the spin-off
FBI_(TV_series)
order is also important for identifying suitable topologies on partially ordered sets, as is done in order theory. Consider any topological space X {\displaystyle
Specialization_preorder
Algebraic structure used in logic
of the terminal object 1 ordered by inclusion, equivalently the morphisms from 1 to the subobject classifier Ω. The open sets of any topological space
Heyting_algebra
Jumper (2008). Set dresser David Ritchie was crushed to death by frozen debris as an exterior set was being dismantled. Law & Order: Special Victims Unit
List of film and television accidents
List_of_film_and_television_accidents
2026 American TV series
television series loosely based on the 1980 novel by A. J. Quinnell. Originally set in Italy/Malta by Quinnell, this series takes place in modern-day Rio De
Man_on_Fire_(TV_series)
Season of American television series
The fourteenth season of Law & Order: Special Victims Unit debuted with a two-part premiere episode on September 26, 2012, at 9pm/8c - 11pm/10c (Eastern)
Law & Order: Special Victims Unit season 14
Law_&_Order:_Special_Victims_Unit_season_14
Russian strategic-level special operations command
The Special Operations Forces of the Armed Forces of the Russian Federation, commonly known as the Special Operations Forces (abbr. SOF; Russian: Силы
Special Operations Forces (Russia)
Special_Operations_Forces_(Russia)
British World War II espionage and sabotage organisation
Special Operations Executive (SOE) was a British organisation formed in 1940 to conduct espionage, sabotage and reconnaissance in German-occupied Europe
Special_Operations_Executive
Motor vehicle
suspension with special springs, shocks, stabilizer bar, and spindle-strut shafts. Since it was competition equipment, the ZR1 could not be ordered with power
Chevrolet_Corvette_(C3)
Iraqi politician (1935–1979)
Baghdad was set in motion by president Saddam and he ordered the event be recorded to set fear in the hearts of all members of the party and set an example
Muhyi_Abdul-Hussein_Mashhadi
Unsolved problem on partial orders
2/3 or better. Equivalently, in every finite partially ordered set that is not totally ordered, there exists a pair of elements x and y with the property
1/3–2/3_conjecture
Diagram that shows all possible logical relations between a collection of sets
every possible way, showing all possible relations between the sets. They are thus a special case of Euler diagrams, which do not necessarily show all relations
Venn_diagram
Season of American television series (2001–2002)
The third season of the television series, Law & Order: Special Victims Unit premiered Friday, September 28, 2001 and ended Friday, May 17, 2002 on NBC
Law & Order: Special Victims Unit season 3
Law_&_Order:_Special_Victims_Unit_season_3
ωε=ε. η 1. The order type of the rational numbers. 2. An eta set, a type of ordered set. 3. ηα is an Erdős cardinal. θ The order type of the real numbers
Glossary_of_set_theory
German assault rifle
respectively). As of March 2012, fielding of 452 IARs had been completed of 4,748 ordered. Five infantry battalions: 1st Light Armored Reconnaissance Battalion and
Heckler_&_Koch_HK416
Joint U.S.-Canadian military unit in WWII
The 1st Special Service Force (FSSF) was an elite joint American–Canadian commando unit in World War II, formed by Lieutenant Colonel Robert T. Frederick
First_Special_Service_Force
Fictional character list
Law & Order: Special Victims Unit, a spin-off of the crime drama Law & Order, follows the detectives who work in the "Special Victims Unit" of the 16th
List of Law & Order: Special Victims Unit characters
List_of_Law_&_Order:_Special_Victims_Unit_characters
2022 lawsuit filed by Donald Trump
grant Trump's request for a special master to review the seized documents for attorney-client and executive privilege and ordered DOJ and Trump to file a
Trump_v._United_States_(2022)
Smallest complete lattice containing a partial order
specifically order theory, the Dedekind–MacNeille completion of a partially ordered set is the smallest complete lattice that contains it. It is named after
Dedekind–MacNeille_completion
Period of supervision over an offender
released from prison on parole. An offender on probation is ordered to follow certain conditions set forth by the court, often under the supervision of a probation
Probation
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
Special Forces Group of the United States Army National Guard
2005, the 1st Special Forces was redesignated as the 1st Special Forces Regiment. On 28 October 2005, 2nd Battalion, 19th SFG(A), was ordered into active
19th_Special_Forces_Group
Special forces police unit
intermediaries. At the very beginning of the Kosovo War, the unit was ordered to set up a temporary base of operations on the Goč mountain, near Kosovo.
Special Operations Unit (Serbia)
Special_Operations_Unit_(Serbia)
Iraqi politician (1966–2003)
as his father's heir apparent in 2000. He was deputy head of the Iraqi Special Security Organization and was also in charge of the Republican Guard, a
Qusay_Hussein
SPECIAL ORDERED-SET
SPECIAL ORDERED-SET
Boy/Male
Indian, Telugu
Special
Girl/Female
Indian
Special
Girl/Female
Bengali, Indian, Telugu
Special
Girl/Female
Hindu, Indian, Tamil
Special
Boy/Male
Hindu, Indian
Special
Girl/Female
Indian
Special
Girl/Female
Hindu, Indian, Tamil
Special
Girl/Female
Greek, Indian, Marathi, Turkish
Special
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’.
Boy/Male
Hindu, Indian
Special
Boy/Male
Hindu
Special
Boy/Male
Indian
Special
Girl/Female
Arabic, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Sindhi, Tamil, Telugu
Special
Girl/Female
Tamil
Special
Girl/Female
Bengali, Indian, Modern
Special
Girl/Female
Bengali, Indian, Telugu
Special
Girl/Female
Hindu, Indian, Tamil
Special
Boy/Male
Tamil
Special
Girl/Female
Indian, Telugu
Special
Boy/Male
Tamil
Saisnigda | ஸாஈஸà¯à®¨à¯€à®•à¯à®¤à®¾
Special
SPECIAL ORDERED-SET
SPECIAL ORDERED-SET
Boy/Male
Muslim
An effect, Impression
Boy/Male
Celebrity, Hindu, Indian, Punjabi, Sanskrit, Sikh, Tamil, Telugu
Endless; Infinite
Male
Native American
Native American Navajo name TSIISHCHILI means "curly-haired."
Boy/Male
Hindu
Lord Shiva
Biblical
a prince; freeborn
Female
English
Modern variant spelling of English Ariana, ARYANA means "utterly pure."
Male
Greek
(Ποσειδῶν) Greek name probably derived from pósis, POSEIDÔN means "lord, husband." In mythology, this is the name of a god of horses and the sea, known as the "earth-shaker." He is equated with Roman Neptune.Â
Boy/Male
Indian
Contended
Girl/Female
Muslim/Islamic
Close to heart Someone who gives guidance, Prophet (saw)'s grand daughter
Girl/Female
Indian, Punjabi, Sikh
Purposeful
SPECIAL ORDERED-SET
SPECIAL ORDERED-SET
SPECIAL ORDERED-SET
SPECIAL ORDERED-SET
SPECIAL ORDERED-SET
a.
Of or pertaining to society; relating to men living in society, or to the public as an aggregate body; as, social interest or concerns; social pleasure; social benefits; social happiness; social duties.
adv.
In a special manner; particularly; especially.
a.
Appropriate; designed for a particular purpose, occasion, or person; as, a special act of Parliament or of Congress; a special sermon.
a.
Being on duty; keeping order; conveying orders.
n.
One appointed for a special service or occasion.
a.
Of or pertaining to the spectrum; made by the spectrum; as, spectral colors; spectral analysis.
a.
Conformed to order; in order; regular; as, an orderly course or plan.
n.
The splenial bone.
n.
One who puts in order, arranges, methodizes, or regulates.
n.
That for which a person is distinguished, in which he is specially versed, or which he makes an object of special attention; a speciality.
a.
Distinguished among others of the same class or kind; special; concerning a species or a single object; principal; particular; as, in an especial manner or degree.
imp. & p. p.
of Order
n.
A sort; a kind; a variety; as, a species of low cunning; a species of generosity; a species of cloth.
a.
Of or pertaining to a species; constituting a species or sort.
a.
Designating the splenial bone.
a.
See Spatial.
a.
Limited in range; confined to a definite field of action, investigation, or discussion; as, a special dictionary of commercial terms; a special branch of study.
n.
One who gives orders.
a.
Observant of order, authority, or rule; hence, obedient; quiet; peaceable; not unruly; as, orderly children; an orderly community.