Identity of the binary operation subtraction is 0
The binary operation subtraction(a,b) is equal to a-b. So, if e is the identity of subtraction, then a-e = a = e-a
by using the first relation(a-e = a), we get e = 0. Is this the identity of subtraction?
e = 0 does not satisfy the second relation a = e-a. If e =0, we get a=-a, which is not correct. So, where did we go wrong?
We started with an assumption that e is the identity of the subtraction. But we found that this is not true. Subtraction does not have identity.