Definition:Non-Comparable Elements

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

Two elements $x, y \in S, x \ne y$ are non-comparable 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
Sometimes this can be found without the hyphen: noncomparable.

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.