# Proof showing the equality of integers

Please help with the following problem. Provide step by step.

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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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.