An Equivalence [[Relation]] is a a form of [[Binary Relation]] that satisfies certain rules that are used to describe 'equivalence' within an algebra / space. $\huge a \sim b $ For a [[Binary Relation]] $R$ on the [[Set|set]] $X$ to be an equivalence relation, it must satisfy the [[Transitive Property]], [[Reflexive Property]] and the [[Symmetric Property]]. $ \huge \begin{align} a \sim a \\ a\sim a &\iff a \sim a\\ a \sim b \wedge b\sim c &\implies a \sim c \end{align} $ Under an equivalence relation, many objects that are not necessarily strictly *equal* may be considered equivalent. All objects in $X$ that are equivalent form an [[Equivalence Class]] under $R$.