Antireflexive Relation/Examples/Distinctness
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Example of Antireflexive Relation
Let $S$ be a set.
Let $\RR$ be the relation on $S$ defined as:
- $\forall x, y \in S: x \mathrel \RR y$ if and only if $x$ is distinct from $y$
Then $\RR$ is antireflexive.
Proof
No element of $S$ is distinct from itself.
Hence the result by definition of distinct.
$\blacksquare$
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): irreflexive