Definition:Strict Total Ordering

Let $$\left({S; \prec}\right)$$ be a relational structure.

Let $$\prec$$ be a strict ordering.

Then $$\prec$$ is a strict total ordering on $$S$$ iff $$\left({S; \prec}\right)$$ has no non-comparable pairs:


 * $$\forall x, y \in S: x \prec y \lor y \prec x$$

That is, iff $$\prec$$ is connected.