Any quantum number that represents the size of an orbital is a positive integer, $n$.
Any quantum number that represents the shape of an orbital is a non-negative integer, $l : l < n$.
Any quantum number that represents the orientation of an orbital, $m$, is an integer such that $|m| \leq l$.
Why do $n$ and $l$ restrict the ranges of $l$ and $m$, respectively?
To be clearer, I ask why the quantum numbers limit each other, not what they signify, which is already explained in the related question: What do the quantum numbers actually signify?
