This paper derives a somewhat surprising but interesting result on the stabilizability of discrete-time parameterized uncertain systems. Contrary to intuition, it shows that the nonlinear growth rate of a discrete-time stabilizable system with linear parameterization is not necessarily small all the time. More specifically, to achieve stabilizability, the system function f(x) = O(vertical bar x vertical bar(b)) with b < 4 is only required for a very tiny fraction of x in R, even if it grows exponentially fast for the other x. This x set is called a regular set, whose density determines the stabilizability of a nonlinear discrete-time control system. The densities of regular sets have also been computed for both stabilizable and unstabilizable systems with scalar parameters. As indicated herein, the density could be extremely sparse, while the corresponding system is stabilizable.