Is the following statement mathematically correct:
$a = +\infty \iff -a = -\infty $
If so, it is the definition of $-\infty$? If not, is there a mathematical proof for it?
My knowledge in maths come from secondary school. I am currently brushing up on sequences. I know that $\bar R$ is $R$ with $+\infty$ and $-\infty$, and that $+\infty$ is the bigger element of this set and $-\infty$ the smallest element of this set. I want to know if it is correct to say: $$\forall a \in \{-\infty, +\infty \}, \forall l \in R^{*}_{-}, \{u_n \to l, v_n \to a \} \implies (u v)_n \to -a$$