Discrete Mathematics & Its Applications. Basic Structures - Sets, Functions, Sequences and Sums

Question

N = {0,1,2,3….} is the set of natural numbers. In Note, it is mentioned that some people do not consider 0 as a natural number.

We know that set of Whole numbers is W = {0,1,2,3...}

My question is :-

If we consider 0 as an element in the set of Natural numbers, then what is the definition of Whole numbers in that scenario?

Comments

definition of “Whole numbers” is also ambiguous like Natural numbers.

As you said some authors include 0 in the set of natural numbers and some don’t.

Likewise, some authors use set $\{0,1,2,3,...\}$ as set of whole numbers and some authors use $\{1,2,3,...\}$ while some authors use $\{…,-3,-2,-1,0,1,2,3,...\}$ as the set of whole numbers.

---

So is natural numbers same as whole numbers if we include 0 ?

---

yes it could be if author doesn’t want to differentiate between these two terms and make the whole theory based on one of these two terms.