Definition:Non-Comparable Elements

Definition
Let $\struct {S, \RR}$ be a relational structure.

Two elements $x, y \in S, x \ne y$ are non-comparable if neither $x \mathrel \RR y$ nor $y \mathrel \RR x$.

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.

If $x$ and $y$ are not non-comparable then they are comparable.