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by simonreiff
16 days ago
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Exactly, so [0]_3 = [3]_3 = [6]_3 = ... (and here these are indeed equalities inside Z/3Z because these are equalities of sets and not just equivalences). And for that reason, we take the "best" or canonical representative of the equivalence class to be [a]_n where 0 is less than or equal to `a`, which is always strictly less than n; hence, [0]_3 is canonical. Actually, since the modulus is often fixed within a computation or expression, we often simply abuse notation by writing: 0 := [0]_n ("zero is defined to be the equivalence class of 0 mod n")
1 := [1]_n
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