# How do you express intervals as inequalities such as (-4,-2)?

Mar 12, 2017

$- 4 < x < - 2$ $: x \in \mathbb{R}$
Let's assume we are dealing with the interval between $- 4$ and $- 2$ on the real line, exclusive of the upper and lower end points.
This means we are considering all points $x$ on the real line between -4 and -2 exclusive. That is all points $x \in R$ where $- 4 < x < - 2$
NB: If we were considering the interval including the upper and lower end points, this could be written: $- 4 \le x \le - 2$ $: x \in \mathbb{R}$