Is $R^N_{ ++}$ a convex set?
I'm working on some optimization hw problems that have some functions of the type: $f:\mathbb{R}^2_{++} \rightarrow \mathbb{R}$
And it seems like in general whenever $\mathbb{R}^N_{++}$ is your domain then, $\bigtriangledown f(x) = 0$ is not satisfied since you're unable to find $x$ values that satisfy that equality.
Could I say that this is true in general for any real valued funtions?