The Universal Approximation Theorem states that:
Let φ(·) be a nonconstant, bounded, and monotonically-increasing continuous function. Let Im0 denote the m0-dimensional unit hypercube [0,1]m0. The space of continuous functions on Im0 is denoted by C(Im0). Then, given any function f Э C(Im0) and є > 0, there exist an integer m1 and sets of real constants αi, bi and wij, where i = 1, …, m1 and j = 1, …, m0 such that we may define:
as an approximate realization of the function f; that is,
for all x1, x2, …, xm0 that lie in the input space.
[ From Wikipedia ]
Beautiful, isn’t? 😛