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13 4 $begingroup$ Relations defined by formulas such as " x has the same age as y" , " x comes from the same country as y " " a has the same image under function f as b " are obviously equivalence relations, due to the presence of the expression " same ... as". Are there many examples of equivalence relations that do not contain this " same ... as" expression and , consequently, that cannot immediately be recognized as equivalence relations ? Are there many examples of equivalence relations that , at first sight, for someone who reads their defining formula for the first time, do not at all look like equivalence relations? What I am looking for is relations such as " a is congruent to b ( modulo n) iff n divides a-b" in which one does not see