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? 

In an algebraic context, many authors use $A^*$ to denote the set $A$ without the zero element.  In your specific example, the author uses $\mathbb Z^*$ to denote the set $\mathbb Z$ without $0$, i.e. $\mathbb Z-\{0\}$. So, $*$ is just used in a context of notation and does not denote any particular operation.
In a similar manner, it also common to write $\mathbb R^*$ for $\mathbb R-\{0\}$, $\mathbb C^*$ for $\mathbb C-\{0\}$, etc.
