# Whole Numbers as a Set

nDever
This question may be a bit elementary and trivial but I am curious.

Throughout my Algebra classes, the definition of whole numbers were inconsistent. First, I was taught that the whole numbers were a subset of real numbers including all natural numbers and zero (non-negative integers), then, I was told that whole numbers included all integers (...-3, -2, -1, 0, 1, 2, 3...).

Is there a universally accepted definition of the set of whole numbers?

Gold Member
MHB
no, there is not. different authors use the term "whole numbers" to mean different things, and because of this, mathematicians usually don't use this term, preferring:

integers
non-negative integers
positive integers

so as to avoid ambiguity.

even the term "natural number" is not consistently used, as some people include 0, but others do not.

nDever
no, there is not. different authors use the term "whole numbers" to mean different things, and because of this, mathematicians usually don't use this term, preferring:

integers
non-negative integers
positive integers

so as to avoid ambiguity.

even the term "natural number" is not consistently used, as some people include 0, but others do not.

So then, terms such as "whole, natural, and counting" do not tend to appear in textbooks?

Elements of $\mathbb{Z}$ are rather called 'integer' numbers than 'whole' numbers.