Question

Question based on Real Analysis?

How to prove that `a +(-a) = 0` where `a in RR` ?

Answer 1

This is an axiom. There is no need of a proof, since it is one of the basic assumptions.

Explanation:

The statement:

`a+(-a) = 0`

follows from the definition of `-a` as the additive inverse of `a`.

It is essentially one of the axioms concerning addition, so is simply a statement of one of the properties of addition as it is defined.