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Whole Numbers as a Set

  1. Nov 25, 2011 #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?
  2. jcsd
  3. Nov 25, 2011 #2


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    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:

    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.
  4. Nov 25, 2011 #3
    So then, terms such as "whole, natural, and counting" do not tend to appear in textbooks?
  5. Nov 25, 2011 #4


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    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".
  6. Nov 26, 2011 #5


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    Homework Helper

    Elements of [itex] \mathbb{Z} [/itex] are rather called 'integer' numbers than 'whole' numbers.
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