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Proposition: Let Q' denote the old construction of the integers and Q denote the new one. The function i: Q' -> Q
is an isomorphism with respect to 0, +, -, *, ', <, i.e., i is bijective and for all x in Q' and y in Q', we have:
i(x) := [x]
i(0Q') = 0Q, i(x+Q'y) = i(x)+Qi(y), i(-Q' x) = -Q i(x), i(x-Q'y) = i(x)-Qi(y), ...
Inverse Isomorphism: j: Q -> Q', j(x) := x0/x1.