1. Let be a set where we can add any two elements and the resulting sum is still an element in the set. (In other words, the set is closed under addition.) Also, two rules about the set are known: , we have +=+. so that , we have + =. Prove that the element is unique.

(Note that all you are allowed to use is that this set is \closed under addition", that addition is commutative, and that there is an element so that += for all in the set, nothing more. For example, there is no such thing as subtraction. )