TITLE: Is this proper notation: $\;\mathbb Z^{+-}\;$?
QUESTION [6 upvotes]: I have a question about notation. Is it okay to represent $\;\mathbb Z^{+-}$ as $ \mathbb Z - \{0\}$ ? 
Like does it make sense to manipulate both sets mathematically like that? ) i.e. $ \{0\} = \mathbb Z - \mathbb Z^{-+} $
Thanks in advance!

REPLY [2 votes]: For your own purposes you can use any notation, but it probably wouldn't be understood by others without qualification. $\mathbb{Z}^*$ stands for the set of invertible integers, while $\mathbb{Z}^{\times}$ means integers except zero. Personally I'd simply write $\mathbb{Z}\setminus 0$, or if you prefer more rigorously $\mathbb{Z} \setminus \{0\}$.