Definition:Non-Comparable Elements

Definition
Let $$\left({S, \mathcal R}\right)$$ be a relational structure.

Two elements $$x, y \in S$$ are non-comparable (or noncomparable) if neither $$x \mathcal R y$$ nor $$y \mathcal R x$$.

The definition is usually used in the context of orderings and preorderings: such a relation is referred to as a partial preordering or partial ordering.

If $$x$$ and $$y$$ are not non-comparable then they are comparable, but the latter term is not so frequently encountered.