Zero is an element of the set of natural numbers?

Answer 1

True or false depending on who you ask. It is a matter of convention. Long ago before people accepted the concept of 0, it wasn't included. Then when people began making formal constructions of the natural numbers in the 19th century they saw that it made a lot of sense (read: it was convenient) to include 0. People are still pretty well split on it today with allegiances sometimes depending on the exact field of the person in question.

If you were to ask me personally: yes yes yes yes yes. But there are people out there who would say no. It comes down to preference of convention. However, as noted already, when you actually try to axiomatically or set theoretically construct the natural numbers, it is almost downright foolish to not include 0 (though of course that is an opinion too, but most people who have studied such constructions would likely agree).