Tag: Additive Identity

Additive identity is its own inverse

by RoRi

Prove that $-0=0$ .

Proof. On the one hand, by Axiom 4, we have,

$-0+0 = -0.$

On the other hand, since $-0$ is the additive inverse of 0, we have,

$-0+0 = 0.$

Therefore,

$-0 = 0. \qquad \blacksquare$