# Totally Ordered Set/Examples

Let $\preccurlyeq$ denote the relation on the set of integers $\Z$ defined as:
$a \preccurlyeq b$ if and only if $0 \le a \le b \text { or } b \le a < 0 \text { or } a < 0 \le b$
where $\le$ is the usual ordering on $\Z$.
Then $\struct {\Z, \preccurlyeq}$ is a totally ordered set.