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    Proof showing the equality of integers

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    Show that equality of integers is an equivalence relation, that is show that equality of integers is reflexive, symmetric, and transitive. Recall two integers z=a--b, w=c--d, a, b, c, d belong to N (natural numbers) are equal if and only if a+d=b+c

    **where a--b and c--d are the set-theoretic interpretation of the symbol a--b is that it is the space of all pairs equivalent to (a,b): a--b is defined as {c,d) belong to NxN: (a,b)~(c,d)}

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    Solution Preview

    Problem: Show that equality of integers is an equivalence relation, that is show that equality of integers is reflexive, symmetric, and transitive. Recall two integers z=a--b, w=c--d, a, b, c, d belong to N (natural numbers) are equal if and only if a+d=b+c

    **where a--b and c--d are the set-theoretic interpretation of the symbol a--b is that it ...

    Solution Summary

    This solution helps provide a proof showing equality of integers is an equivalence relation, and shows that equality of integers is reflexive, symmetric and transitive. The explanation is given step by step.

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