(Review) Equivalence Relation

Let R be a binary relation on S.

Then R is an equivalence relation on S iff

R is reflexive on S.

R is symmetric

R is transitive

Example. Let’s say that two positive integers x and y not equal to 1 have the same base if there exist three integers b, m, and n such that x = bm and y = bn.

So 36 and 216 have the same base, because 36 = 62 and 216 = 63.

The relation of having the same base is an equivalence relation.

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