Definition:Relation/Notation

Notation for Relation

Let $\RR$ be a relation.

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

• Definition:Complement of Relation

Sources

• 1979: John E. Hopcroft and Jeffrey D. Ullman: Introduction to Automata Theory, Languages, and Computation ... (previous) ... (next): Chapter $1$: Preliminaries: $1.5$ Relations
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): relation: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): relation: 1.
• 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