>> Next, let's say that if A-B and B-C are connected, then A-C
>> are too.
>
> No. That's only generally true for equality relations.
>
> Equivalence relations are not equality relations.

Actually, transitivity is a requirement for an equivalence relation.
(In addition to symmetry (A~B => B~A) and reflexivity (A~A for all
A).)

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