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.