Neural networks are commonly used for classification tasks, in fact from this [post][1] it seems like that's where they shine brightest.  

When we want to classify using NNs, we just take the **last** layer to take values in $[0,1]$; typically, by taking the last layer to be the *sigmoid* function $x \mapsto \frac{e^x}{e^x +1}$.  Is this theoretically justified?  (i.e., is there an analogue to the [universal approximation theorem][2] for this case)?



  [1]: https://ai.stackexchange.com/q/18576/2444
  [2]: https://en.wikipedia.org/wiki/Universal_approximation_theorem