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Mathematical phrase
In mathematics, the phrase complete partial order is variously used to refer to at least three similar, but distinct, classes of partially ordered sets
Complete_partial_order
Mathematical set with an ordering
especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other. The word partial is used
Partially_ordered_set
Existence of certain infima or suprema of a given poset
familiar example is the completeness of the real numbers. A special use of the term refers to complete partial orders or complete lattices. However, many
Completeness_(order_theory)
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
Glossary of terms used in branch of mathematics
(infima) exist. Complete partial order. A complete partial order, or cpo, is a directed complete partial order (q.v.) with least element. Complete relation.
Glossary_of_order_theory
Topic in automated planning
Partial-order planning is an approach to automated planning that maintains a partial ordering between actions and only commits ordering between actions
Partial-order_planning
Topics referred to by the same term
ordered set Complete partial order Permutation, the act of arranging all the members of a set into some sequence or order Ranking Stochastic ordering of random
Order
mathematics, a partial cyclic order is a ternary relation that generalizes a cyclic order in the same way that a partial order generalizes a linear order. Over
Partial_cyclic_order
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
Ordinal number Well-quasi-ordering Semilattice Lattice (Directed) complete partial order, (d)cpo Bounded complete Complete lattice Knaster–Tarski theorem
List_of_order_theory_topics
Set whose pairs have minima and maxima
are seen as complete lattices, complete join-semilattices, complete meet-semilattices, or as join-complete or meet-complete lattices. "Partial lattice" is
Lattice_(order)
Partially ordered set in which all subsets have both a supremum and infimum
see completeness). Another usage of "complete meet-semilattice" refers to a meet-semilattice that is bounded complete and a complete partial order. This
Complete_lattice
On chains and antichains in partial orders
needed to cover all elements. This number is called the width of the partial order. The theorem is named for the mathematician Robert P. Dilworth, who
Dilworth's_theorem
Mathematical ordering of a partial order
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 order
Linear_extension
In mathematics, a first-order partial differential equation is a partial differential equation that involves the first derivatives of an unknown function
First-order partial differential equation
First-order_partial_differential_equation
mathematical fields of order and domain theory, a Scott domain is an algebraic, bounded-complete and directed-complete partial order (dcpo). They are named
Scott_domain
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
Branch of mathematics
set is also a partial order in which every two distinct elements are incomparable. It is also the only relation that is both a partial order and an equivalence
Order_theory
Mathematical concept for comparing objects
)} , the set of natural numbers with standard ordering, is a well partial order (in fact, a well-order). However, ( Z , ≤ ) {\displaystyle (\mathbb {Z}
Well-quasi-ordering
bound also have a least upper bound. Such a partial order can also be called consistently or coherently complete (Visser 2004, p. 182), since any upper bound
Bounded_complete_poset
Surgical removal of a kidney
than one gram per kilogram body weight per day in order to reduce the long-term risk of CKD. Partial nephrectomy is the surgical removal of a kidney tumor
Nephrectomy
Nonempty, upper-bounded, downward-closed subset
and definitions such as "ideal", "order ideal", "Frink ideal", or "partial order ideal" mean one another. An important special case of an ideal is constituted
Ideal_(order_theory)
Topics referred to by the same term
to: Dame Commander of the Order of Pope Pius IX, a class of the papal order of knighthood Directed complete partial order, in mathematics This disambiguation
DCPO
Theorem in order theory and lattice theory
Suppose ( L , ⊑ ) {\displaystyle (L,\sqsubseteq )} is a directed-complete partial order (dcpo) with a least element, and let f : L → L {\displaystyle f:L\to
Kleene_fixed-point_theorem
Subset of incomparable elements
define the height of a partial order to be the maximum cardinality of a chain. Mirsky's theorem states that in any partial order of finite height, the
Antichain
Order-preserving mathematical function
{\displaystyle \leq } denote the partial order relation of any partially ordered set, a monotone function, also called isotone, or order-preserving, satisfies the
Monotonic_function
Topics referred to by the same term
United States Postal Service Complete partial order, a term used in mathematical order theory Compulsory purchase order, a legal function in the UK and
CPO
Definition of continuity for functions between posets
_{Q}f(B)} . A subset of a directed complete partial order is closed with respect to the Scott topology induced by the partial order if and only if it is a lower
Scott_continuity
Topological space whose topology is fully captured by its lattice of open sets
makes the specialization preorder a directed complete partial order. Every continuous directed complete poset equipped with the Scott topology is sober
Sober_space
Mathematical measure for partial orders
rise to the partial order. This concept is also sometimes called the order dimension or the Dushnik–Miller dimension of the partial order. Dushnik & Miller
Order_dimension
Well-quasi-ordering of finite trees
reverse mathematics as a statement that cannot be proved in ATR0 (a second-order arithmetic theory with a form of arithmetical transfinite recursion). In
Kruskal's_tree_theorem
Term in the mathematical area of order theory
order isomorphism. Since partial orders are antisymmetric, the only ones that are self-dual are the equivalence relations (but the notion of partial order
Duality_(order_theory)
Alternative mathematical ordering
a cyclic order if it is cyclic, asymmetric, transitive, and connected. Dropping the "connected" requirement results in a partial cyclic order. A set with
Cyclic_order
Non-zero element of a matrix selected by an algorithm
times that of partial pivoting and is therefore cheaper than complete pivoting. Rook pivoting has been proved to be more stable than partial pivoting both
Pivot_element
Mathematical ranking of a set
< x {\displaystyle y<x} is true. A strict partial order < {\displaystyle \,<\,} is a strict weak ordering if and only if incomparability with respect
Weak_ordering
Algebraic object with an ordered structure
higher-order, viewing positive cones as maximal prepositive cones provides a larger context in which field orderings are extremal partial orderings. A field
Ordered_field
Instantaneous rate of change (mathematics)
{\displaystyle \partial _{x}f} , ∂ ∂ x f {\displaystyle {\frac {\partial }{\partial x}}f} , or ∂ f ∂ x {\displaystyle {\frac {\partial f}{\partial x}}}
Derivative
Concept in order theory
every pair, possesses a meet and a join is a complete lattice. It is also possible to define a partial lattice, in which not all pairs have a meet or
Join_and_meet
Relaxed variant of the sorting problem
its elements all appear in order, while partial sorting is returning a list of the k smallest (or k largest) elements in order. The other elements (above
Partial_sorting
axiom, 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
Reflexive and transitive binary relation
relations and (non-strict) partial orders. Both of these are special cases of a preorder: an antisymmetric preorder is a partial order, and a symmetric preorder
Preorder
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List of minor planets: 5001–6000
List_of_minor_planets:_5001–6000
Smallest complete lattice containing a partial order
example of a partial ordering is the inclusion ordering ⊆ on pairs of sets. If S is a partially ordered set, a completion of S means a complete lattice L
Dedekind–MacNeille_completion
Rational fractions as sums of simple terms
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the
Partial fraction decomposition
Partial_fraction_decomposition
Visual depiction of a partially ordered set
whether it has a non-crossing Hasse diagram. It is NP-complete to determine whether a partial order with multiple sources and sinks can be drawn as a crossing-free
Hasse_diagram
Class of mathematical orderings
the set of possible order types is uncountable. Tree (set theory), generalization Ordinal number Well-founded set Well partial order Prewellordering Directed
Well-order
⊆ D is directed if ∀ x,y ∈ X ∃ z ∈ X where x≤ z & y ≤ z. D is a complete partial order (cpo) if: ⋅ Every directed X ⊆D has a supremum, and: ∃ bottom element
Computable_topology
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List of minor planets: 8001–9000
List_of_minor_planets:_8001–9000
Partial order with joins
to this partial order. A lattice is a partially ordered set that is both a meet- and join-semilattice with respect to the same partial order. Algebraically
Semilattice
Relationship between elements of two sets
preorder. The MacNeille completion theorem (1937) (that any partial order may be embedded in a complete lattice) is cited in a 2013 survey article "Decomposition
Binary_relation
Subset of a preorder that contains all larger elements
upper set containing all minimal elements of Y . {\displaystyle Y.} For partial orders satisfying the descending chain condition, antichains and upper
Upper_and_lower_sets
Nonlinear second-order partial differential equation of special kind
Monge–Ampère equation is a nonlinear second-order partial differential equation of special kind. A second-order equation for the unknown function u {\displaystyle
Monge–Ampère_equation
Sequence of spaces in linear algebra
flag is called a complete flag if di = i for all i, otherwise it is called a partial flag. A partial flag can be obtained from a complete flag by deleting
Flag_(linear_algebra)
Standard for assessing computer system vulnerabilities
value of "Partial+" for Confidentiality, Integrity, and Availability, to fill perceived gaps in the description between Partial and Complete in the official
Common Vulnerability Scoring System
Common_Vulnerability_Scoring_System
ordered sets (or posets), orderings in which some pairs are comparable and others might not be Preorders, a generalization of partial orders allowing ties
List of order structures in mathematics
List_of_order_structures_in_mathematics
value Polymorphism Calculus of constructions Domain theory Directed complete partial order Knaster–Tarski theorem Cartesian closed category Yoneda lemma Graph
List of functional programming topics
List_of_functional_programming_topics
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
Theories in mathematical logic
\partial (uv)=u\,\partial v+v\,\partial u} ∀ u ∀ v ∂ ( u + v ) = ∂ u + ∂ v . {\displaystyle \forall u\forall v\,\partial (u+v)=\partial u+\partial v\
List_of_first-order_theories
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
Ordered_vector_space
Smallest transitive relation containing a given binary relation
acyclic graph (DAG) is the reachability relation of the DAG and a strict partial order. The transitive closure of an undirected graph produces a cluster graph
Transitive_closure
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
Algorithmic paradigm for constraint satisfaction or enumeration problems
which admit the concept of a "partial candidate solution" and a relatively quick test of whether it can possibly be completed to a valid solution. It is
Backtracking
Complete Tear Partial Tear (Type 6) Step Two: Assessment pyramidalis-adductor longus connection Normal Complete Tear Partial Tear Step Three: Partial
Pyramidalis–anterior pubic ligament–adductor longus complex
Pyramidalis–anterior_pubic_ligament–adductor_longus_complex
Study of programming languages via mathematical objects
of partial functions from N {\displaystyle \mathbb {N} } to N {\displaystyle \mathbb {N} } . Partial functions form a chain-complete partial order using
Denotational_semantics
Graph linking pairs of comparable elements in a partial order
and order theory, a comparability graph is an undirected graph that connects pairs of elements that are comparable to each other in a partial order. Comparability
Comparability_graph
Mathematical proposition equivalent to the axiom of choice
The word "partial" is meant to indicate that not every pair of elements of a partially ordered set is required to be comparable under the order relation
Zorn's_lemma
Special subset of a partially ordered set
preordering to associated partial ordering. Historically, filters generalized to order-theoretic lattices before arbitrary partial orders. In the case of
Filter_(mathematics)
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List of minor planets: 4001–5000
List_of_minor_planets:_4001–5000
1990 book on mathematical order theory
and Galois connections on partial orders, and the Dedekind–MacNeille completion of a partial order into the smallest complete lattice containing it. The
Introduction to Lattices and Order
Introduction_to_Lattices_and_Order
Mathematical ordering with upper bounds
\supseteq ,\,} define partial orders on any given family of sets. A non-empty family of sets is a directed set with respect to the partial order ⊇ {\displaystyle
Directed_set
Seizures which affect only one brain hemisphere
consciousness seizures (formerly known as complex partial seizures) are characterized by a reduction or complete loss of awareness and responsiveness during
Focal_seizure
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List of minor planets: 3001–4000
List_of_minor_planets:_3001–4000
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List of minor planets: 6001–7000
List_of_minor_planets:_6001–7000
2025 United States Supreme Court case
Inc. (1999). The Court granted the government a partial stay of the injunctions blocking Executive Order 14160, but "only to the extent that the injunctions
Trump_v._CASA
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List of minor planets: 2001–3000
List_of_minor_planets:_2001–3000
Mathematical result on order relations
proved by Edward Szpilrajn in 1930, states that every partial order is contained in a total order. Intuitively, the theorem says that any method of comparing
Szpilrajn_extension_theorem
Node ordering for directed acyclic graphs
order that is compatible with it, in the sense that, if x ≤ y in the partial order, then x ≤ y in the total order as well. One can define a partial ordering
Topological_sorting
Surgical procedure to remove a fetus from the uterus
describes an intact D&E on a live fetus as a partial-birth abortion, the procedure is uncommon. The 2003 federal Partial-Birth Abortion Ban Act, which was upheld
Intact dilation and extraction
Intact_dilation_and_extraction
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
Localized dielectric breakdown under high voltage stress
In electrical engineering, partial discharge (PD) is a localized dielectric breakdown (DB) (which does not completely bridge the space between the two
Partial_discharge
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List of minor planets: 10001–11000
List_of_minor_planets:_10001–11000
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
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List of minor planets: 11001–12000
List_of_minor_planets:_11001–12000
Decomposed form of dislocation that occurs within a crystalline material
between partial dislocations. Conversely, low stacking fault energy materials will have large distances between partial dislocations. In order to cross
Partial_dislocation
Set theory concept
theory, a club set is a subset of a limit ordinal that is closed under the order topology, and is unbounded (see below) relative to the limit ordinal. The
Club_set
Numerical ordering with a margin of error
strict weak orderings, in which items with equal scores may be tied but there is no margin of error. They are a special case of partial orders and of
Semiorder
Differential equation important in physics
The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves
Wave_equation
Differential equation containing derivatives with respect to only one variable
derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations (PDEs) which may be with respect to more than one
Ordinary differential equation
Ordinary_differential_equation
Isomorphism type of ordered sets
With respect to their standard ordering as numbers, the set of rationals is not well-ordered. Neither is the completed set of reals, for that matter.
Order_type
Optimality condition in optimal control theory
stochastic systems, in which case the HJB equation is a second-order elliptic partial differential equation. A major drawback, however, is that the HJB
Hamilton–Jacobi–Bellman equation
Hamilton–Jacobi–Bellman_equation
Partially ordered vector space, ordered as a lattice
pointwise partial order is a Dedekind complete Riesz space. The space R 2 {\displaystyle \mathbb {R} ^{2}} with the lexicographical order is a non-Archimedean
Riesz_space
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List_of_minor_planets:_9001–10000
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List of minor planets: 7001–8000
List_of_minor_planets:_7001–8000
Unsolved problem on partial orders
and at most 2/3 of the linear extensions of the partial order place x earlier than y. The partial order formed by three elements a, b, and c with a single
1/3–2/3_conjecture
Term in finance
focuses on "complete vs. partial fulfillment", whereas the latter hinges on the immediacy of the transaction. If you place an AON order requesting 100
All_or_none
Special type of lattice
construct a topological space with an additional partial order on its points, yielding a (completely order-separated) ordered Stone space (or Priestley space)
Distributive_lattice
Mathematical result or axiom on order relations
collection of sets, the relation "is a proper subset of" is a strict partial order on A. Suppose that A is the collection of all circular regions (interiors
Hausdorff_maximal_principle
Partial differential equation
the inviscid Burgers' equation, being a first-order partial differential equation, also has a complete integral which contains two arbitrary constants
Burgers'_equation
Equivalence of partially ordered sets
the order) it would follow that x ≤ y {\displaystyle x\leq y} and y ≤ x {\displaystyle y\leq x} , implying by the definition of a partial order that
Order_isomorphism
Event wherein the Sun is obscured by the Moon
detaching mountings will have. In the partial eclipse path, one will not be able to see the corona or nearly complete darkening of the sky. However, depending
Solar_eclipse
COMPLETE PARTIAL-ORDER
COMPLETE PARTIAL-ORDER
Male
English
English form of Roman Latin Martialis, MARTIAL means "of/like Mars."
Boy/Male
Tamil
Complete
Male
German
German form of French Percevel, PARZIVAL means "pierced valley."
Boy/Male
Teutonic
Martial ruler.
Girl/Female
Australian, French, Greek
Victory of the People
Boy/Male
Hindu, Indian
Lord of Parti; One of the Name of Shri Satya Saibaba
Boy/Male
Latin
Warring.
Boy/Male
Tamil
Complete
Girl/Female
Tamil
Complete
Girl/Female
Tamil
Complete
Boy/Male
Hindu
Lord of parti one of the name of Shri Satya Sai baba
Male
Spanish
Spanish form of Roman Latin Martialis, MARCIAL means "of/like Mars."
Male
German
Variant spelling of German Parzifal, PARSIFAL means "pierced valley."
Female
English
English Shakespeare character name derived from Roman Latin Porcius, PORTIA means "pig." A moon of Uranus was given this name.
Male
German
German form of French Percevel, PARZIFAL means "pierced valley."
Boy/Male
Tamil
Poornan | பூரà¯à®¨à®¾à®¨
Complete
Poornan | பூரà¯à®¨à®¾à®¨
Boy/Male
Australian, Christian, French, Latin, Swiss
Warring; Like Mars; Roman God Mars
Girl/Female
Hindu, Indian
Queen
Girl/Female
Latin American Shakespearean
An offering. Portia was a heroine in Shakespeare's 'The Merchant of Venice'.
Male
Hungarian
Hungarian form of Greek Bartholomaios, BARTAL means "son of Talmai."
COMPLETE PARTIAL-ORDER
COMPLETE PARTIAL-ORDER
Girl/Female
Muslim/Islamic
Light of the moon
Boy/Male
Assamese, Indian
Egg Plant
Girl/Female
English
Feminine of Ned.
Male
German
Variant spelling of German Haimo, HEIMO means "home."
Boy/Male
Hindu
The enriched one, Prosperous
Boy/Male
Arabic, Muslim
Period
Girl/Female
Greek
Of the west wind.
Boy/Male
Indian
Having Hair Like Lion
Girl/Female
Persian
Happiness.
Surname or Lastname
English
English : from Old French corde ‘string’, a metonymic occupational name for a maker of cord or string, or a nickname for an habitual wearer of decorative ties and ribbons.French : variant of Couard, a derogatory nickname from Old French couard ‘coward’, ‘poltroon’, a compound of coe ‘tail’ + the pejorative suffix -ard.
COMPLETE PARTIAL-ORDER
COMPLETE PARTIAL-ORDER
COMPLETE PARTIAL-ORDER
COMPLETE PARTIAL-ORDER
COMPLETE PARTIAL-ORDER
imp. & p. p.
of Compete
n.
Paralysis, complete or partial. See Paralysis.
n.
An incomplete or partial shadow.
a.
Of, pertaining to, or suited for, war; military; as, martial music; a martial appearance.
a.
Belonging to war, or to an army and navy; -- opposed to civil; as, martial law; a court-martial.
a.
Finished; ended; concluded; completed; as, the edifice is complete.
v. t.
To bring to a state in which there is no deficiency; to perfect; to consummate; to accomplish; to fulfill; to finish; as, to complete a task, or a poem; to complete a course of education.
a.
Incomplete.
imp. & p. p.
of Complete
pl.
of Court-martial
adv.
In a complete manner; fully.
a.
Making complete.
n.
A patrial noun. Thus Romanus, a Roman, and Troas, a woman of Troy, are patrial nouns, or patrials.
a.
Complex, complicated.
n.
Pertaining to a subordinate portion; as, a compound umbel is made up of a several partial umbels; a leaflet is often supported by a partial petiole.
a.
Impartial.
a.
Pertaining to, or containing, iron; chalybeate; as, martial preparations.
n.
Of, pertaining to, or affecting, a part only; not general or universal; not total or entire; as, a partial eclipse of the moon.
n.
An incomplete or partial dislocation.
adv.
In a partial manner; with undue bias of mind; with unjust favor or dislike; as, to judge partially.