Given real numbers $a$ and $b$ satisfying $a \leq b$, define:
$$\langle a,b\rangle (x) = \mathrm{min}(b,\mathrm{max}(a,x)) = \mathrm{max}(a,\mathrm{min}(b,x))$$
(These numbers are equal because $a \leq b$. See here for some relevant abstract generalities.)
So basically, the function $$\langle a,b\rangle : \mathbb{R} \rightarrow \mathbb{R}$$ has the effect of "truncating" a real number so as to lie in the interval $[a,b]$.
This function shows up implicitly in one of my applied math homework assignments. We're modelling the amount of fluid in a reservoir; due to rainfall or evaporation, the volume changes, but it always remains between $0$ and $V_\mathrm{max}$, and hence the function $\langle 0,V_\mathrm{max}\rangle$ implicitly shows up in our numerical model.
I'll bet the function $\langle a,b\rangle$ shows up all over applied math, so:
Question. Does this function have an accepted name or notation?