Asymmetric Relation/Examples

Examples of Asymmetric Relations

Parent

Asymmetric Relation/Examples/Parent

Greater Than

The relation $\RR$ defined on the set of real numbers $\R$:

$\forall x, y \in \R: x \mathop \RR y \iff x > y$

where:

$>$ denotes the conventional greater than relation

is an asymmetric relation.

Less Than

The relation $\RR$ defined on the set of real numbers $\R$:

$\forall x, y \in \R: x \mathop \RR y \iff x < y$

where:

$<$ denotes the conventional less than relation

is an asymmetric relation.