The Universal Approximation Theorem states that:

Let φ(·) be a nonconstant, bounded, and monotonically-increasing continuous function. Let I_m0 denote the m₀-dimensional unit hypercube [0,1]^m₀. The space of continuous functions on I_m0 is denoted by C(I_m0). Then, given any function f Э C(I_m0) and є > 0, there exist an integer m₁ and sets of real constants α_i, b_i and w_ij, 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, …, x_m0 that lie in the input space.

[ From Wikipedia ]

Beautiful, isn’t? 😛