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  2. Relation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Relation_(mathematics)

    For example, "is a blood relative of" is a symmetric relation, because x is a blood relative of y if and only if y is a blood relative of x. Antisymmetric for all x, y ∈ X, if xRy and yRx then x = y. For example, ≥ is an antisymmetric relation; so is >, but vacuously (the condition in the definition is always false). [11] Asymmetric

  3. Connected relation - Wikipedia

    en.wikipedia.org/wiki/Connected_relation

    For example, that every equivalence relation is symmetric, but not necessarily antisymmetric, is indicated by in the "Symmetric" column and in the "Antisymmetric" column, respectively. All definitions tacitly require the homogeneous relation R {\displaystyle R} be transitive : for all a , b , c , {\displaystyle a,b,c,} if a R b {\displaystyle ...

  4. Finitary relation - Wikipedia

    en.wikipedia.org/wiki/Finitary_relation

    Computer scientists, logicians, and mathematicians, however, tend to have different conceptions what a general relation is, and what it is consisted of. For example, databases are designed to deal with empirical data, which is by definition finite, whereas in mathematics, relations with infinite arity (i.e., infinitary relation) are also ...

  5. Category:Mathematical relations - Wikipedia

    en.wikipedia.org/wiki/Category:Mathematical...

    Printable version; In other projects ... often as expressed in the axioms or definitions that they satisfy. Many of these types of relations are listed below ...

  6. List of set identities and relations - Wikipedia

    en.wikipedia.org/wiki/List_of_set_identities_and...

    In constructive mathematics, "not empty" and "inhabited" are not equivalent: every inhabited set is not empty but the converse is not always guaranteed; that is, in constructive mathematics, a set that is not empty (where by definition, "is empty" means that the statement () is true) might not have an inhabitant (which is an such that ).

  7. Converse relation - Wikipedia

    en.wikipedia.org/wiki/Converse_relation

    For example, the converse of the relation 'child of' is the relation 'parent of'. In formal terms, if X {\displaystyle X} and Y {\displaystyle Y} are sets and L ⊆ X × Y {\displaystyle L\subseteq X\times Y} is a relation from X {\displaystyle X} to Y , {\displaystyle Y,} then L T {\displaystyle L^{\operatorname {T} }} is the relation defined ...

  8. Transitive relation - Wikipedia

    en.wikipedia.org/wiki/Transitive_relation

    In mathematics, a binary relation R on a set X is transitive if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c. Every partial order and every equivalence relation is transitive. For example, less than and equality among real numbers are both transitive: If a < b and b < c then a < c; and if x ...

  9. Relation algebra - Wikipedia

    en.wikipedia.org/wiki/Relation_algebra

    In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation.The motivating example of a relation algebra is the algebra 2 X 2 of all binary relations on a set X, that is, subsets of the cartesian square X 2, with R•S interpreted as the usual composition of binary relations R and S, and with the ...

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