For every function $f$:$\{0,1{\}}^{100}\{0,1\},$ there exists a Feedforward

Neural Network $N($with Step Function activation functions$)$ such that

$f(x_1,...,x_{100})=N(x_1,...,x_{100})$ for all $(x_1,$dots,$x_{100})in\{0,1{\}}^{100}.$

For every continuous function $f$:$[0,1{]}^{100}[0,1],$ there exists a

Feedforward Neural Network $N($with Sigmoid activation functions$)$ such that

$f(x_1,...,x_{100})=N(x_1,...,x_{100})$ for all $(x_1,...,x_{100})in[0,1{]}^{100}.$