TITLE: Is $0$ a natural number?
QUESTION [144 upvotes]: Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number?
It seems as though formerly $0$ was considered in the set of natural numbers, but now it seems more common to see definitions saying that the natural numbers are precisely the positive integers.

REPLY [2 votes]: The Peano-Dedekind axioms (as used in proving propositions by use of the Principle of Mathematical Induction) define the $\mathbb{N}$ as either $\mathbb{N}$ = $\mathbb{Z^+} \cup \text{0} = \text{{0, 1, 2, ...}}$ or $\mathbb{N} = \mathbb{Z^+} = \text{{1, 2, 3, ...}}$, that is, it depends on the context (usually this "context" may be seen from the given proposition to be proved, at least in the case of using PMI).