Can a neural network with only $1$ hidden layer solve any problem? Can a network with a single hidden layer of $N$ neurons (where $N\le\infty$) approximate any arbitrary function so that this network’s error approaches $0$ as $N$ approaches $\infty$?

More comments about "network’s error approaches 0"
There is an important concept about Bayes error rate. Even most powerful model may achieve very high error rates, just because there are large irreducible error.
As an example example, think about if we have large amount of data that have exactly same feature but different label.
