Inverse for Real Addition

Theorem
Each element $x$ of the set of real numbers $\R$ has an inverse element $-x$ under the operation of real number addition:
 * $\forall x \in \R: \exists -x \in \R: x + \paren {-x} = 0 = \paren {-x} + x$

Proof
We have:

Similarly for $\paren {-\eqclass {\sequence {x_n} } {} } + \eqclass {\sequence {x_n} } {}$.

Thus the inverse of $x \in \struct {\R, +}$ is $-x$.