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 $x \mathrel {\mathcal R} y$ nor $y \mathrel {\mathcal R} x$.

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

Also known as
Some use the term incomparable.

Also see
The definition is usually used in the context of orderings and preorderings.

Such a relation with non-comparable pairs is referred to as a partial preordering or partial ordering.