This is a question, of what would be "formally more correct".
Let's assume I have a random function, say $f(x)=x^3-3x^2-9x+27$.
This function has the extremes $P=(3|0)$ -> local minimum, $Q=(-1|32)$ -> local maximum. An extreme means a shift in monotony ($-$ the slope of the tangent line is equal to $0$ there).
If I want to write down, where this function is (strictly) monotonically increasing/decreasing, how should I go about this?
Should I write
$(-\infty, -1)$ - strictly monotonically increasing (open interval)
OR
$(-\infty, -1]$ - monotonically increasing (half-open interval).
What seems more intuitive to you?