Final answer:
A proof demonstrating that a set forms a group under addition.
Step-by-step explanation:
In order to show that the set A forms a group under addition, we need to prove four properties: closure, associativity, identity element, and inverses.
Closure:
For any two elements a and b in A, their sum a + b will also be in A. This is true because ordinary addition is commutative, meaning that a + b = b + a.
Associativity:
For any three elements a, b, and c in A, the sum is associative, meaning that (a + b) + c = a + (b + c).
Identity Element:
The identity element is the element 0, where 0 + a = a for any element a in A.
Inverses:
For any element a in A, there exists an inverse element -a such that a + (-a) = 0.