what does it mean that a pure virtual function has no body?

Question

and why cant it have a body?

Answer 1

It can't have a body partially because that is how it's defined.... but that's too circular to be useful.

Why would you do that? To provide a safe set of methods that other classes know they can call on subclasses of the abstract class can call. Then, you make fully fleshed out subclasses that are interchangeable so you can compare solutions, or switch the type of calculations you're doing depending on the situation.