Name of the set of negative integers

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  • #1
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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?
 

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  • #2
Hurkyl
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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).
 
  • #3
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Ugh, it would seem logical that it would have a name independent of denoting a particular part of Z.
 
  • #4
CRGreathouse
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Ugh, it would seem logical that it would have a name independent of denoting a particular part of Z.
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.
 
  • #5
HallsofIvy
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Ugh, it would seem logical that it would have a name independent of denoting a particular part of Z.
Why would that seem logical? What do you perceive as the reason for "naming" sets of numbers?
 
  • #6
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Why would that seem logical? What do you perceive as the reason for "naming" sets of numbers?
Because the negative integers are not the non-negative integers?
 
  • #7
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Actually N often denotes the positive integers, which again begs the question of why does labeling any set of numbers matter at all.
 
  • #8
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Actually N often denotes the positive integers, which again begs the question of why does labeling any set of numbers matter at all.
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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