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Proof about Integers and Rationals

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Show that the definition of negation on the integers is well-defined in the sense that if (a----b)=(a'----b'), then -(a----b)= -(a'----b') (so equal integers have equal negations)

where a----b is the space of all pairs equivalent to (a,b)

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The expert provides proof about integers and rationals.

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Suppose [(a,b)]=[(a',b')]. Show that -[(a,b)]=-[(a',b')].
Proof: Let ~ be an equivalence relation on the set of ordered pairs of natural numbers N×N ...

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