The symbol ℤ represents the set of integers, and so g: ℤ → ℤ represents a function that takes integers as inputs and
produces integers as outputs. supose that a function g: ℤ → ℤ satisfies g(a + b) = g(a) + g(b) for al integers a
and b. is there necesarily an integer k such that g(n) = k for al integer inputs n?
a. let k = g(1). compute g(2) and g(3).
b. let n be any positive integer. compute g(n).
c. now, consider g(0). since g(0) = g(0 + 0), what can you conclude about g(0)?
d. lastly, use the fact that g(n + −n) = g(0) to learn something about g(−n), where n is any positive integer.
e. use your work above to prove that g(n) = k for every integer n. be sure to consider the fact that n could be
positive, negative, or 0.