Whole Numbers as a Set

  • Thread starter nDever
  • Start date
  • #1
nDever
76
1
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

  • #2
Deveno
Science Advisor
Gold Member
MHB
2,725
6
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
nDever
76
1
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?
 
  • #4
Deveno
Science Advisor
Gold Member
MHB
2,725
6
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
dextercioby
Science Advisor
Homework Helper
Insights Author
13,238
994
Elements of [itex] \mathbb{Z} [/itex] are rather called 'integer' numbers than 'whole' numbers.
 

Suggested for: Whole Numbers as a Set

Replies
9
Views
9K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
30
Views
4K
  • Last Post
Replies
3
Views
887
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
5
Views
2K
Replies
1
Views
2K
Replies
2
Views
802
Replies
3
Views
869
Top