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Isomorphism of Integer Constructions

Proposition: Let Z' denote the old construction of the integers and Z denote the new one. The function i: Z' -> Z

i(x) := [x]
is an isomorphism with respect to 0, +, -, *, <, i.e., i is bijective and for all x in Z' and y in Z', we have:
i(0Z') = 0Z,
i(x+Z'y) = i(x)+Zi(y),
i(-Z' x) = -Z i(x),
i(x-Z'y) = i(x)-Zi(y),

Inverse Isomorphism: j: Z -> Z', j(x) := I(x)

Author: Wolfgang Schreiner
Last Modification: January 12, 2000

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