Definition:Relation/Class Theory

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Definition

Let $V$ be a basic universe.

In the context of class theory, a relation $\RR$ is a subclass of the Cartesian product $V \times V$.


Notation

If $\tuple {x, y}$ is an ordered pair such that $\tuple {x, y} \in \RR$, we use the notation:

$s \mathrel \RR t$

or:

$\map \RR {s, t}$

and can say:

$s$ bears $\RR$ to $t$
$s$ stands in the relation $\RR$ to $t$


If $\tuple {s, t} \notin \RR$, we can write: $s \not \mathrel \RR t$, that is, by drawing a line through the relation symbol.

See Complement of Relation.


Sources