Totally Ordered Set/Examples
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Examples of Totally Ordered Sets
Example Ordering on Integers
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.