Definition:Non-Comparable Elements

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

Two elements $$x, y \in S$$ are non-comparable 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.