Name of the set of negative integers

[G037H3]

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?

 

[Hurkyl]

I don't recall seeing it given a specific name. I sometimes see decorations like

$$\def\ZZ{\mathbb{Z}} \ZZ^+ \, \ZZ^> \, \ZZ^{\geq} \, \ZZ^- \, \ZZ^{\leq}$$​

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).

 

[G037H3]

Ugh, it would seem logical that it would have a name independent of denoting a particular part of Z.

 

[CRGreathouse]

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 $$\mathbb{Z}^{<}$$ and write m.

 

[HallsofIvy]

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?

 

[G037H3]

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?

 

[snipez90]

Actually N often denotes the positive integers, which again begs the question of why does labeling any set of numbers matter at all.

 

[G037H3]

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 ;)