this post was submitted on 22 Jul 2024
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No, it's correct. You define the operation by it's properties. It's not saying that "a plus 0 = a" but "the result of applying the binary operation '+' to any number with 0 should give the original number."
You have to have previously defined 1=S(0), 2=S(1), 3=S(2), and so on.