Interval notation: infinity, -infinity in closed interval

Question

I was watching a video stream a little bit ago and noticed on an equation without context that had the interval $\left[{-\infty, \infty}\right]$. This was preculiar to me as I've never seen the interval for $\mathbb{R}$ expressed this way before, however, I do vaguely remember hearing something about this a long time ago and its use in the construction of certain uncountably infinite sets in axiomatic set theory, but I'm not sure. Is there any use in writing ${-\infty, \infty}$ in a closed interval? If so, what would its use be?

Answer 1

$[-\infty,+\infty]$ refers to the extended reals. In general, though, $\mathbb{R}=(-\infty,+\infty)$.