neural networks

Hi, I am trying to understand neural networks with a feeble mind. I was
watching a presentation where they talk about using neural networks for
function approximation. I don't know about this but it seems that
neural networks are themselves some type of function (technically I
guess that is true since they map inputs into outputs -not sure if they
do that uniquely or not..).
What is a mathematical description of this type of function? I mean,
you take the inputs, assign weights, get an output which then becomes
an input and so on. It seems like a kind of composition of like a step
function or something. Does anyone have any information or insight in
this?
Thanks very much.

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