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Reversal of the order of elements of a binary relation
the converse of a binary relation is the relation that occurs when the order of the elements is switched in the relation. For example, the converse of
Converse_relation
Concept in mathematical logic
{\displaystyle R} is a binary relation with R ⊆ A × B , {\displaystyle R\subseteq A\times B,} then the converse relation R T = { ( b , a ) : ( a , b )
Converse_(logic)
Relationship between elements of two sets
{\displaystyle \leq } . The complement of the converse relation R T {\displaystyle R^{\textsf {T}}} is the converse of the complement: R T ¯ = R ¯ T . {\displaystyle
Binary_relation
Type of residuated Boolean algebra with extra structure
relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation. The motivating example of a relation
Relation_algebra
Relationship between two sets, defined by a set of ordered pairs
relations includes the operations of taking the converse and composing relations. The above concept of relation has been generalized to admit relations between
Relation_(mathematics)
Pairs of words that refer to a relationship from opposite points of view
borrow/lend. The relationship between such words is called a converse relation. Converses can be understood as a pair of words where one word implies a
Converse_(semantics)
Type of logical relation
binary relation R ⊆ X×Y between two sets X and Y is total (or left total) if the source set X equals the domain {x : there is a y with xRy }. Conversely, R
Total_relation
Type of binary relation
sets are well-founded. A relation R is converse well-founded, upwards well-founded, or Noetherian on X, if the converse relation R−1 is well-founded on
Well-founded_relation
Topics referred to by the same term
Converse relation or inverse relation, in mathematics the relation that occurs when switching the order of the elements in a binary relation Converse
Converse
Property of a relation on a set
complementary relation of R {\displaystyle R} , I {\displaystyle I} is the identity relation and R ⊤ {\displaystyle R^{\top }} is the converse relation of R {\displaystyle
Connected_relation
Binary relation over a set and itself
Boolean algebra augmented with the involution of mapping of a relation to its converse relation. Considering composition of relations as a binary operation
Homogeneous_relation
Mathematical set with an ordering
of a partial order relation R {\displaystyle R} is defined by letting R op {\displaystyle R^{\text{op}}} be the converse relation of R {\displaystyle
Partially_ordered_set
Topics referred to by the same term
inverse relation may refer to: Converse relation or "transpose", in set theory Negative relationship, in statistics Inverse proportionality Relation between
Inverse_relation
Operation on binary relations
R\mathbin {;} (S\mathbin {;} T)=(R\mathbin {;} S)\mathbin {;} T.} The converse relation of R ; S {\displaystyle R\mathbin {;} S} is ( R ; S ) T = S T ; R
Composition_of_relations
Any one of the distinct objects that make up a set in set theory
membership only, and "includes" for the subset relation only. For the relation ∈ , the converse relation ∈T may be written A ∋ x {\displaystyle A\ni x}
Element_of_a_set
Directed graph with reversed edges
vertices. The converse relation of a binary relation is the relation that reverses the ordering of each pair of related objects. If the relation is interpreted
Transpose_graph
Multivalued function in mathematics
logarithm, is a multivalued function, namely the branches of the converse relation of the function f ( w ) = w e w {\displaystyle f(w)=we^{w}} , where
Lambert_W_function
Branch of mathematics
Mathematics (1903). Russell noted that binary relation aRb has a sense proceeding from a to b with the converse relation having an opposite sense, and sense "is
Order_theory
Descriptive set theory relation
that a relation R {\displaystyle R} is a countable Borel relation between X {\displaystyle X} and Y {\displaystyle Y} but the converse relation is not
Countable_Borel_relation
Reflexive and transitive binary relation
vertices, and the order relation between pairs of elements corresponding to the directed edges between vertices. The converse is not true: most directed
Preorder
Function that is its own inverse
of binary relations, every relation has a converse relation. Since the converse of the converse is the original relation, the conversion operation is
Involution_(mathematics)
Relation of degree three
Within the calculus of relations each relation A has a converse relation AT and a complement relation A. Using these involutions, Augustus De Morgan and Ernst
Ternary_relation
Reasoning about equations with free variables
the converse relation that always exists, contrary to function theory. A given relation may be represented by a logical matrix; then the converse relation
Algebraic_logic
Type of binary relation
transitivity when in a relation there are no ordered pairs of the form (a,b) and (b,c). The converse (inverse) of a transitive relation is always transitive
Transitive_relation
Relationship between objects
Sometimes the word-object relation is called "denotation"; the word denotes the object. The converse relation, the relation from object to word, is called
Reference
One-to-one correspondence
domain X (indicated by f: X → Y in functional notation) also defines a converse relation starting in Y and going to X (by turning the arrows around). The process
Bijection
is a proper subset of B {\displaystyle B} . ⊃, ⊇, ⊋ Denote the converse relation of ⊂ {\displaystyle \subset } , ⊆ {\displaystyle \subseteq } , and
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Type of abstract object
binary relation has a converse relation, and the converse of ∈ {\displaystyle \in } is written ∋ {\displaystyle \ni } . Also, a binary relation must have
Domain_of_discourse
Type of binary relation
A symmetric relation is a type of binary relation. A homogeneous relation R {\displaystyle R} on a set X {\displaystyle X} is symmetric if: for all a
Symmetric_relation
Topics referred to by the same term
rule of replacement in philosophical logic Transpose relation, another name for converse relation Transposition (chess), different moves or a different
Transposition
Semigroup in abstract algebra
relations between a set and itself, with the involution being the converse relation, and the multiplication given by the usual composition of relations
Semigroup_with_involution
Mathematical concept
is a special type of binary relation, many of the properties of an inverse function correspond to properties of converse relations. If an inverse function
Inverse_function
where R is a relation. Barbara A mnemonic for a certain syllogism. class A subset of the members of some type codomain The codomain of a relation R is the
Glossary of Principia Mathematica
Glossary_of_Principia_Mathematica
Category whose objects are sets and whose morphisms are binary relations
so it is the converse relation. Thus Rel contains its opposite and is self-dual. The involution represented by taking the converse relation provides the
Category_of_relations
Topics referred to by the same term
Converse relation of a partial order is sometimes called its order dual. Also called its dual order or its transpose, inverse, opposite, or converse.
Order_dual
Matrix operation which flips a matrix over its diagonal
matrix, the transpose of the cofactor matrix Conjugate transpose Converse relation Moore–Penrose pseudoinverse Projection (linear algebra) Nykamp, Duane
Transpose
Schema in modal logic
on a symmetric accessibility relation, then the Barcan formula will be valid in the frame if, and only if, the converse Barcan formula is valid in the
Barcan_formula
Concept that is not defined in terms of previously defined concepts
Regarding relations, Russell takes as primitive notions the converse relation and complementary relation of a given xRy. Furthermore, logical products of relations
Primitive_notion
Formal system for transcribing expressions into equivalent terms
{*}{\leftarrow }}} are closures of ← {\displaystyle {\leftarrow }} , the converse relation of → {\displaystyle {\rightarrow }} . ↔ {\displaystyle \leftrightarrow
Abstract_rewriting_system
Pattern defining an infinite sequence of numbers
difference equation can be associated to every recurrence relation, and, conversely, a recurrence relation can be associated to every difference equation such
Recurrence_relation
Mathematical operation that combines three elements to produce another element
r]=pq^{T}r} where q T {\displaystyle q^{T}} is the converse relation of q. Properties of this ternary relation have been used to set the axioms for a heap.
Ternary_operation
Foundational principle in quantum physics
possible momentum components the particle could have are more widespread. Conversely, the more localized the momentum-space wavefunction, the more likely the
Uncertainty_principle
converse relation, R T . {\displaystyle R^{\operatorname {T} }.} Transitive closure – Smallest transitive relation containing a given binary relation
Symmetric_closure
Term in the mathematical area of order theory
equivalence relations (but the notion of partial order is self-dual). Converse relation List of Boolean algebra topics Transpose graph Duality in category
Duality_(order_theory)
Matrix of binary truth values
logical matrix R {\displaystyle R} of a binary relation corresponds to the converse relation. The binary relation R on the set {1, 2, 3, 4} is defined so that
Logical_matrix
Web of human social relationships
people. For example, if x is the parent of y, the relation may be symbolized as xPy. The converse relation, that y is the child of x, is written yPTx. Suppose
Kinship
relations, and the anti-involution of R {\displaystyle R} is the converse relation R ∘ {\displaystyle R^{\circ }} ; we have y R ∘ x {\displaystyle yR^{\circ
Allegory_(mathematics)
Mathematical concept for comparing objects
the normal subgroups). Any equivalence relation is the negation of an apartness relation, though the converse statement only holds in classical mathematics
Equivalence_relation
Ways how entities stand to each other
the order in which the elements are related to each other. The converse of a relation carries the same information and has the opposite direction, like
Relation_(philosophy)
Concept in projective geometry
I) to obtain the dual structure C∗ = (L, P, I∗), where I∗ is the converse relation of I. C∗ is also a projective plane, called the dual plane of C. If
Duality_(projective_geometry)
Relation between vapour pressure and temperature
The Clausius–Clapeyron relation, in chemical thermodynamics, specifies the temperature dependence of pressure, most importantly vapor pressure, at a discontinuous
Clausius–Clapeyron_relation
Overview of and topical guide to logic
Congruence relation Connected relation Converse relation Coreflexive relation Covering relation Cyclic order Dense relation Dependence relation Dependency
Outline_of_logic
General concept and operation in mathematics
the dual poset Pd = (X, ≥) comprises the same ground set but the converse relation. Familiar examples of dual partial orders include the subset and superset
Duality_(mathematics)
Generalised concept of incidence structure of polygons
notion of points and lines reversed and the incidence relation taken to be the converse relation of I {\displaystyle I} . It can easily be shown that this
Generalized_polygon
Type of fallacious argument (logical fallacy)
propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal
Affirming_the_consequent
Structure in group theory (in mathematics)
functional inverse defined from image to domain (equivalently, the converse relation). This is the "archetypal" inverse semigroup, in the same way that
Inverse_semigroup
Geometric concept of a 2D space with "points at infinity" adjoined
I) we obtain the dual structure C* = (L, P, I*), where I* is the converse relation of I. In a projective plane a statement involving points, lines and
Projective_plane
Number of orderings allowing ties
a(n)=3} derived relations. These are the given relation y = f ( x ) {\displaystyle y=f(x)} , the converse relation x = f ( y ) {\displaystyle x=f(y)} obtained
Ordered_Bell_number
Relation between sides of a right triangle
mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states
Pythagorean_theorem
Abstract mathematical system of two types of objects and a relation between them
( L , P , I ∗ ) {\displaystyle C^{*}=(L,P,I^{*})} where I∗ is the converse relation of I. It follows immediately from the definition that: C ∗ ∗ = C {\displaystyle
Incidence_structure
Type of mathematical relation
condition of analyticity, and conversely, analyticity implies causality of the corresponding stable physical system. The relation is named in honor of Ralph
Kramers–Kronig_relations
Finite sets whose elements are all hereditarily finite sets
{\text{BIT}}^{\top })} (where BIT ⊤ {\displaystyle {\text{BIT}}^{\top }} is the converse relation of BIT {\displaystyle {\text{BIT}}} , swapping its two arguments)
Hereditarily_finite_set
Binary relation which never occurs in both directions
asymmetric, and the converse or dual > {\displaystyle \,>\,} of < {\displaystyle \,<\,} is also asymmetric. An asymmetric relation need not have the connex
Asymmetric_relation
Concept in modal logic
In quantified modal logic, the Buridan formula and the converse Buridan formula (more accurately, schemata rather than formulas) (i) syntactically state
Buridan_formula
Concept in topology
B} then A {\displaystyle A} and B {\displaystyle B} are close, but the converse is not true. closeness between a point and a set is preserved by continuous
Closeness_(mathematics)
Type of psychological relationship
that is seen as being engaging, directly addressing the audience, and conversing with them in a friendly and personal manner. By viewing media personas
Parasocial_interaction
Algebraic structure with a ternary operation
q T r {\displaystyle [p,q,r]=pq^{\mathrm {T} }r} where qT is the converse relation of q. The result of this composition is also in B ( A , B ) {\displaystyle
Heap_(mathematics)
Mathematical relation inside orderings
mathematics, especially order theory, the covering relation of a partially ordered set is the binary relation which holds between comparable elements that are
Covering_relation
Set whose elements all belong to another set
true of every set A that A ⊂ A . {\displaystyle A\subset A.} (a reflexive relation). Other authors prefer to use the symbols ⊂ {\displaystyle \subset } and
Subset
Description of aspects of ontology
ontology is expressed. An important type of relation is the subsumption relation (is-a-superclass-of, the converse of is-a, is-a-subtype-of or is-a-subclass-of)
Ontology_components
Smallest transitive relation containing a given binary relation
only if, R itself is transitive. Conversely, transitive reduction reduces a minimal relation S from a given relation R such that they have the same closure
Transitive_closure
Formula in classical differential geometry
In classical differential geometry, Clairaut's relation, named after Alexis Claude de Clairaut, is a formula that characterizes the great circle paths
Clairaut's relation (differential geometry)
Clairaut's_relation_(differential_geometry)
Mathematical tool for studying knots
the converse is not true. Skein relations are often used to give a simple definition of knot polynomials. A skein relation gives a linear relation between
Skein_relation
ordering. The converse, the symmetric closure, the reflexive closure, and the transitive closure of a rewrite relation is again a rewrite relation, as are the
Rewrite_order
A prime p divides a^p–a for any integer a
group theory. The converse of Fermat's little theorem fails for Carmichael numbers. However, a slightly weaker variant of the converse is Lehmer's theorem:
Fermat's_little_theorem
Glossary of terms used in branch of mathematics
of the form {x in P | x ≤ a} is a finite set. Inverse. See converse. Irreflexive. A relation R on a set X is irreflexive, if there is no element x in X
Glossary_of_order_theory
Theorem about right triangles
{pq}}} or in term of areas: h 2 = p q . {\displaystyle h^{2}=pq.} The converse statement is true as well. Any triangle, in which the altitude equals the
Geometric_mean_theorem
Symbol connecting formulas in logic
for biconditional in Łukasiewicz in 1929. Such a logical connective as converse implication " ← {\displaystyle \leftarrow } " is actually the same as material
Logical_connective
Operation on the subsets of a set
smallest relation on A {\displaystyle A} that contains R {\displaystyle R} and is closed under this partial binary operation. A preorder is a relation that
Closure_(mathematics)
Function that preserves distinctness
{\displaystyle g} is called a retraction of f {\displaystyle f} . Conversely, f {\displaystyle f} is called a section of g {\displaystyle g} . For
Injective_function
Type of binary relation
the converse also holds. Dually, each right Euclidean relation is right quasi-reflexive, and each right unique and right quasi-reflexive relation is right
Euclidean_relation
Informal fallacy
The fallacy of converse accident is an informal fallacy that occurs when a rule that applies only to an exceptional case is wrongly applied to all cases
Converse_accident
Set of the elements not in a given subset
logical matrix of the complement. Together with composition of relations and converse relations, complementary relations and the algebra of sets are the elementary
Complement_(set_theory)
Order whose elements are all comparable
which any two elements are comparable. That is, a total order is a binary relation ≤ {\displaystyle \leq } on some set X {\displaystyle X} , which satisfies
Total_order
Strong, deep, or close association or acquaintance between two or more people
In social psychology, an interpersonal relation (or interpersonal relationship) describes a social association, connection, or affiliation between two
Interpersonal_relationship
Direct conversion of temperature differences to electric voltage and vice versa
creates a voltage when there is a different temperature on each side. Conversely, when a voltage is applied to it, heat is transferred from one side to
Thermoelectric_effect
Solution of some Diophantine equation
theorem, says: Every computably enumerable set is Diophantine, and the converse. Equivalently to the definition given above, a set S of integers is computably
Diophantine_set
Evolution of a word's meaning
generalization), "sibling-of" relation, and "contrast-to" relation (for antiphrasis, auto-antonymy, and auto-converse), respectively in Blank (1997) and Blank (1999)
Semantic_change
Logical inference from a single statement
", one can make the immediate inference that "No P are S" which is the converse of the given statement. Given a type I statement, "Some S are P.", one
Immediate_inference
Concept in Marxism
wage worker's consequent relation to the capitalist; a feudal lord's relationship to a fief, and the serf's consequent relation to the lord; a slavemaster's
Relations_of_production
Visual depiction of a partially ordered set
different meaning: the directed acyclic graph obtained from the covering relation of a partially ordered set, independently of any drawing of that graph
Hasse_diagram
Binary relation in computer science
{\displaystyle D} . The independency relation is symmetric and irreflexive. Conversely, given any symmetric and irreflexive relation I {\displaystyle I} on a finite
Dependency_relation
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
Type of sexual desire in psychoanalytic theory
Saussure introduced the term in 1920 by way of analogy to its logical converse in psychoanalysis, the Oedipus complex, and it may be used to cover different
Jocasta_complex
Mathematical relation making a non-equal comparison
In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often
Inequality_(mathematics)
Basic notion of sameness in mathematics
into disjoint equivalence classes. Conversely, every partition defines an equivalence class. The equivalence relation of equality is a special case, as
Equality_(mathematics)
Ancient Greek concept of spiritedness
Homeric hero is under emotional stress, he may externalize his thumos and converse with or scold it. Achilles, in the Iliad, cares for his own honour; he
Thumos
insufficient sample, fallacy of the lonely fact, hasty induction, secundum quid, converse accident, jumping to conclusions) – basing a broad conclusion on a small
List_of_fallacies
complement is. Similarly, a relation is quasitransitive if, and only if, its converse is. Intransitivity Reflexive relation Robert Duncan Luce (Apr 1956)
Quasitransitive_relation
Semantic relation of a part to the whole
(from Ancient Greek ὅλος (hólos) 'whole' and ὄνυμα (ónuma) 'name') is the converse of meronymy. A closely related concept is that of mereology, which specifically
Meronymy_and_holonymy
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