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## Homework Statement

Find the range of the function g: ZxZ --> ZxZ given by g(m,n)=(m-n,m+n). Hints: First recall that if f: A ---> B then Range (f)={b e B such that there exists an A in A with b=f(a). Second, if you claim that some set C is the range, then you must show that i) C is a subset Range(f) and ii) range (f) is a subset of C. Both i and ii are required to conclude that C=range(f).

## Homework Equations

none

## The Attempt at a Solution

I am think that the range is all integers from -infinity to +infinity.

I know that:

* ZxZ denotes a set of ordered pairs.

* m,n exist in Z

* range (g) exists in Z

I don't know where to go with this!