What does $*$ mean in equivalence relations? The notation of "$*$" started being used in my proof textbook in the section of equivalence relations and partitions yet it never once said what it means. 
An example from the textbook: 
Let $\mathbb{Z}^* = \mathbb{Z} - \{0\}.$ Define the relation on $\mathbb{Z} \times \mathbb{Z^*}$ by, for all $a,c \in \mathbb{Z}$ and all $b,d \in \mathbb{Z}$ 
What does "$*$" mean? 

The notation refers to all non-zero elementes, in your case, of the integers $\mathbb Z$. As it is defined by excluding $0$ from the integers by $\mathbb Z^*=\mathbb Z-\{0\}=\mathbb Z\setminus\{0\}$.
