Supremum and infimum of an inequality I feel like this is elementary but I can't seem to determine the supremum/infimum (if they exist) of the following example: 
Let $S = \{x \in \mathbb{R} : x^2 > 2x + 8\}$
I rewrote it as $$x^2 -2x - 8 > 0$$
$$(x-4)(x+2) > 0 $$
So it is clear that there is no supremum. 
But how do I determine the infimum?
Thanks in advance.

$S = (-\infty,-2)\cup (4,\infty)$, thus $\inf(S) = -\infty$, and $\sup(S) = \infty$.
