Question

Do natural numbers have to be positive?

Answer 1

In mathematics, natural numbers are the ordinary counting numbers 1, 2, 3, ... (sometimes zero is also included). There is no universal agreement about which set of numbers is designated by the term "natural numbers": some use it to designate the positive integers {1, 2, 3, ...}, others include the number 0, so that the term designates the non-negative integers {0, 1, 2, 3, ...}. The former definition is the traditional one, the use of the latter definition appears first in the 19th century. Some authors use the term natural number to exclude zero and whole number to include it; others use whole number in a way that excludes zero, or in a way that includes both zero and the negative integers.

Answer 2

In simple terms, yes.