That is a good example. But you are forgetting that neural networks are approximating the actual functions, so the function you described could be built with so

That is a good example. But you are forgetting that neural networks are approximating the actual functions, so the function you described could be built with some kind of confidence level in the answer. Just like you can have some confidence that certain code will not halt from experience, neural network could also be built to do that. Not all possible functions though, unless you have infinitely large network with infinite computing power.