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▮ Teino "n": | Katy Perry [(m1, m2)]: ~ n': | Examples: the integers, the Grothendieck group of a manifold and of a ring: Now when we use the Grothendieck group construction we obtain the formal differences between natural numbers as elements n - m and we have the equivalence relation: n - m ~ n' - m' ⇔ n + m' = n'+ m.