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Example

• The difference of 5 and 3 is denoted by

  I(5_N, 3_N) = <2_N, 0_N> = 2_Z.

• The difference of 3 and 5 is denoted by

  I(3_N, 5_N) = <0_N, 2_N> = -2_Z.

Now it remains to define the arithmetic operations.