Equivalence Relation/Examples/Non-Equivalence/Divisor Relation
Example of Relation which is not Equivalence
Let $x \divides y$ denote that $x$ is a divisor of $y$
Then $\divides$ is not an equivalence relation.
From Divisor Relation on Positive Integers is Partial Ordering we have that $\divides$ is reflexive and transitive.
But we have:
- $2 \divides 4$
- $4 \nmid 2$