Set Equivalence behaves like Equivalence Relation/Warning

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Set Equivalence behaves like Equivalence Relation: Warning

It has been shown that set equivalence exhibits the same properties as an equivalence relation.

However, it is important to note that set equivalence is not strictly speaking a relation.

This is because the collection of all sets is itself specifically not a set, but a class.

Hence it is incorrect to refer to $\sim$ as an equivalence relation, although it is useful to be able to consider it as behaving like an equivalence relation.