# Mathematical relationship definition wikipedia

### Relation (mathematics) - Simple English Wikipedia, the free encyclopedia

In mathematics, a function was originally the idealization of how a varying quantity depends on .. This is often used in relation with the arrow notation for elements (read: "f maps x to f (x)"), often stacked immediately below the arrow notation. Mathematical relations fall into various types according to their specific properties , often as expressed in the axioms or definitions that they satisfy. Many of these. In the mathematics of binary relations, the composition relations is a concept of forming a new relation S ∘ R from two given relations R and S. The composition.

The set of all functions is a subset of the set of all relations - a function is a relation where the first value of every tuple is unique through the set. Other well-known relations are the Equivalence relation and the Order relation.

That way, sets of things can be ordered: Take the first element of a set, it is either equal to the element looked for, or there is an order relation that can be used to classify it.

## Composition of relations

That way, the whole set can be classified compared to some arbitrarily chosen element. Relations can be transitive.

One example of a transitive relation is "smaller-than". One example of a symmetric relation is "is equal to". If X "is equal to" Y, Y "is equal to" X.

One example of an anti-symmetric relation is if "X is equal Y", "Y is not equal to X". Relations can be reflexive. A relation is asymmetric if and only if it is both anti-symmetric and irreflexive.

For example, "is ancestor of" is transitive, while "is parent of" is not. A transitive relation is irreflexive if and only if it is asymmetric.

## Relationship

This property is sometimes called "total", which is distinct from the definitions of "total" given in the previous section. Every reflexive relation is serial: This makes sense only if relations on proper classes are allowed.

Well-foundedness implies the descending chain condition that is, no infinite chain R x3 R x2 R x1 can exist. If the axiom of choice is assumed, both conditions are equivalent. A relation that is reflexive, symmetric, and transitive is called an equivalence relation. A relation that is symmetric, transitive, and serial is also reflexive.

### Relation - Wikipedia

A relation that is only symmetric and transitive without necessarily being reflexive is called a partial equivalence relation. A relation that is reflexive, antisymmetric, and transitive is called a partial order.

Ancient Greeks[ edit ] Traditionally the history of the concept of relation begins with Aristotle and his concept of relative terms.

In Metaphysics he states: These were later redefined as "categorical" propositions in order to distinguish them from two other types of proposition, the disjunctive and the hypothetical, identified a little later by Chrysippus. A fundamental opposition was developing between substance and relation.