Definition:Finer Equivalence Relation
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Let $X$ be a set.
Let $\equiv$ and $\sim$ be equivalence relations on $X$.
Then $\equiv$ is finer than $\sim$ if and only if:
- $\forall x, y \in X : x \equiv y \implies x \sim y$
Also known as
If $\equiv$ is finer than $\sim$, then $\sim$ is said to be coarser than $\equiv$.