This is a chapter from a textbook, one that seems pretty introductory at that. I'd say it is a pretty important piece of information to convey and prove, this a

This is a chapter from a textbook, one that seems pretty introductory at that. I'd say it is a pretty important piece of information to convey and prove, this ability of neural networks to represent any function. Seems to me that jumping to whether they can "learn any function" as you asked, would certainly have come after this is first established.