Is zero a natural number?

[polymath257]

Zero does not have any positive or negative value so zero cannot be a natural number. But it sure is a whole number

0 is greater than or equal to 0. it is also less than or equal to 0.

Whether 0 is included as a natural number is simply a matter of convention and convenience. In computer science, it is often useful to have an offset of 0 and so many situations begin counting at 0.

In set theory, it is convenient to define 0 as the empty set and natural numbers in terms of transitive sets. So the standard definition has 0 as a natural number.

The axioms of Peano arithmetic are slightly different depending on whether you want to have 0 or 1 be the smallest natural number.

Most algebraic systems (rings, fields, semi-rings, abelian groups, commutative monoids) have an additive identity element and it is convenient to have such. So 0 tends to be in most systems.

The natural numbers, if they include 0 are a very important example of a semi-ring. Without 0, they are not.

So, it is usually convenient to include 0 as a natural number.