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

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Answer 1 · 2017-08-27T22:59:31

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

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.