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Let $\RR$ be a relation.
Two elements $x \in \Dom \RR$, $y \in \Img \RR$ such that $x \ne y$ 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.
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.
- 1968: A.N. Kolmogorov and S.V. Fomin: Introductory Real Analysis ... (previous) ... (next): $\S 3.3$: Ordered sets. Order types