Equivalence Relation/Examples/Equality

Example of Equivalence Relation

Let $S$ be a set.

Let the relation $\RR$ on $S$ be defined as:

$\forall x, y \in S: x \mathrel \RR y \iff x = y$

that is, the equality relation on $S$.

Then $\RR$ is an equivalence relation.


Proof

Demonstrated in Diagonal Relation is Equivalence.

$\blacksquare$


Sources

  • 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.
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