What's the common ground of all numerical and analytical techniques for nonlinear problems?

In this paper the author attempts to find out in very general meanings the common ground of all numerical and analytical techniques for nonlinear problems. By means of analyzing the finiteness or infiniteness of the fundamental operations necessary for mathematically solving a problem, the author points out that the key of any nonlinear technique is the way to transform a nonlinear problem to an infinite series of sub-problems which can be solved by finite number of fundamental operations.