# Whole Numbers as a Set

## Main Question or Discussion Point

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?

## Answers and Replies

Deveno
Science Advisor
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.

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?

Deveno
Science Advisor
on the contrary, they often do. but what sets these are may vary from textbook to textbook (different conventions), there is no "universally used definition".

dextercioby
Science Advisor
Homework Helper
Elements of $\mathbb{Z}$ are rather called 'integer' numbers than 'whole' numbers.