Why is a rational number defined as a cartesian product of Z × (Z \ {0}) and not Z × (N \ {0})?
Why is a rational number defined as a cartesian product of Z × (Z \ {0}) and not Z × (N \ {0})?
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Why is a rational number defined as a cartesian product of Z × (Z \ {0}) and not Z × (N \ {0})?
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Look at how division of rationals is defined: (a/b) / (c/d) = (a*d) / (b*c)
This definition works alone if (b*c) is allowed to be negative.
Example: (1/2) / (-3*4) = (4 / -6)