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Name of the set of negative integers

  1. Sep 4, 2010 #1
    I know that N (natural numbers) is the set of non-negative integers, 0, 1, 2, 3, 4...infinity, and that Z is the set of all integers, both positive and negative. But what is the name or representation of the set of negative integers?
  2. jcsd
  3. Sep 4, 2010 #2


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    I don't recall seeing it given a specific name. I sometimes see decorations like
    [tex]\def\ZZ{\mathbb{Z}} \ZZ^+ \, \ZZ^> \, \ZZ^{\geq} \, \ZZ^- \, \ZZ^{\leq}[/tex]​
    to specify various subsets of the integers (the positive elements, the elements greater than 0, the elements greater-than-or-equal-to zero, et cetera).
  4. Sep 4, 2010 #3
    Ugh, it would seem logical that it would have a name independent of denoting a particular part of Z.
  5. Sep 4, 2010 #4


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    Yeah, it really doesn't have one. Frankly it's more common to pull an element n from N and write -n, rather than pull an element m from [tex]\mathbb{Z}^{<}[/tex] and write m.
  6. Sep 5, 2010 #5


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    Why would that seem logical? What do you perceive as the reason for "naming" sets of numbers?
  7. Sep 8, 2010 #6
    Because the negative integers are not the non-negative integers?
  8. Sep 8, 2010 #7
    Actually N often denotes the positive integers, which again begs the question of why does labeling any set of numbers matter at all.
  9. Sep 9, 2010 #8
    There is no strong convention, but Euler considers 0 to be part of the set of natural numbers; I'll go with him on it ;)
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