Equivalence Class/Relation

An equivalence class is a subset of a larger set containing elements that are considered "equivalent" to eachother in the context of a equivalence relation. An equivalence relation is a binary operation denoted $a \sim b$ that satisfies three fundamental properties: - (Reflexivity) $a \sim a$ - (Symmetry) If $a \sim b$, then $b \sim a$ - (Transitivity) If $a \sim b$ and $b \sim c$, then $a \sim c$