Definition:Non-Comparable

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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.


Sources