Let $\backslash varphi(\backslash cdot)$ be a nonconstant, bounded, and monotonically-increasing continuous function. Let $I\_m$ denote the ''m''-dimensional unit hypercube $()^m$. The space of continuous functions on $I\_m$ is denoted by $C(I\_m)$. Then, given any function $f\backslash in\; C(I\_m)$ and $\backslash varepsilon>0$, there exists an integer $N$ and real constants $v\_i,b\_i\backslash in\backslash mathbb$, where $i=1,\backslash cdots,N$ such that we may define:
: $$
F( x ) =
\sum_^ v_i \varphi \left( w_i^T x + b_i\right)

as an approximate realization of the function $f$ where $f$ is independent of $\backslash varphi$; that is,
: $$
| F( x ) - f ( x ) | < \varepsilon

for all $x\backslash in\; I\_m$. In other words, functions of the form $F(x)$ are dense in $C(I\_m)$.