Definition:Relation/Class Theory
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Definition
Let $V$ be a basic universe.
Let $A$ and $B$ be subclasses of $V$.
A relation $\RR$ is a subclass of the Cartesian product $A \times B$.
Note that in this context either or both of $A$ and $B$ can be $V$ itself.
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.
Also see
- Results about relations can be found here.
Sources
- 2010: Raymond M. Smullyan and Melvin Fitting: Set Theory and the Continuum Problem (revised ed.) ... (previous) ... (next): Chapter $2$: Some Basics of Class-Set Theory: $\S 8$ Relations