# Whole Numbers as a Set

1. Nov 25, 2011

### 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?

2. Nov 25, 2011

### Deveno

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.

3. Nov 25, 2011

### nDever

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

4. Nov 25, 2011

### Deveno

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".

5. Nov 26, 2011

### dextercioby

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