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"Two's Compliment represents a linear automorphism over a cyclic group" is what I think you're trying to say. russdill & co are hinting that Modular Arithmetics are cyclic groups.

I think for most people, the aha-moment comes when they realize One's Compliment double-counts the zero. In contrast, linearity is simply assumed. Otherwise, why would anyone make a number system out of it?






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