For an equivalence relation $\sim$ what is $\mathbb{R}/{\sim}$? I mean explicitly and formally...
2026-04-06 14:40:07.1775486407
$\mathbb{R}/{\sim}$: A Question about the Formal Definition of a Quotient
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Define on $\mathbb R$ an equivalence relation $\sim$ that's reflexive, symmetric and transitive and for all $x\in \mathbb R$ let $$[x]=\{y\in\mathbb R\ |\ y\sim x\}$$ the class of $x$ i.e. the set of element in relation with $x$, hence it isn't difficult to prove that the set of classes denoted by $\mathbb R/\sim$ $$\mathbb R/\sim=\{[x]\ |\ x\in\mathbb R\}$$ forms a partition of $\mathbb R$.