Relation

A relation describes as a connection between the elements of a Set, and that may or may not hold between two elements of that set.

For example, in the set of natural numbers, the relation “is less than” does not hold between 5 and 4, but it does between 4 and 5.

Formal Definition

Given a set $X$, a relation $R$ over $X$ is a set of Ordered Pairs of elements from $X$, then:

$R\subseteq \{(x,y)|x,y\in X\}$

The statement $(x,y)\in R$ reads ”$x$ is $R$-related to $y$”, and is written in the infix notation as $xRy$. The order of elements is important, because if $x\ne y$, then $yRx$ can be true or false independently of $xRy$.

Related

• Finitary Relation (a relation on the Cartesian Product of a number of sets)
• Binary Relation (a widely studied finitary relation in which the number of sets is 2)