How useful is Turing completeness? are neural nets turing complete?

Question

While reading some papers about the Turing completeness of recurrent neural nets (for example: Turing computability with neural nets, Hava T. Siegelmann and Eduardo D. Sontag, 1

Answer 1

To partially address your second question:

Neural Networks have the property of being universal approximators - that is, they can approximate any function to an arbitrary degree of precision. It's the "degree of precision" part that keeps the Neural Network from needing to be infinite.