Why is –(–a) = a?
The Additive Inverse states that if a number belongs to the set of real numbers, then its
opposite exists and the sum of the number and its opposite is equal to the identity
element. Using numbers, that means if 5 is a real number, then –5 is a real number and
5 + (–5) = 0.
Now let’s start with –5 being a real number. By the Additive Inverse, the opposite of –5
is a real number. That means –(–5) is a real number and –5 + –(–5) = 0
Now we have 5 + (–5) = 0 and –5 + –(–5) = 0. Since both these equal zero, by
substitution, the expressions are equal.
5 + (–5) =–5 + –(–5). If I add +5 to both sides, I am left with 5 = –(–5)
Now, everywhere I used a 5, plug in “a” to answer the original question.