Comparable Elements

Suppose <= is a partial ordering on a nonempty set A. Then the elements a,b in A are said to be comparable provided a<=b or b<=a.

Because two elements in a partially ordered set need not be comparable, it is possible for a partially ordered set to have more than one maximal element. For example, suppose we have a nonempty partially ordered set A in which every element is incomparable to every other element, i.e., A is totally unordered. It follows that every element of A is maximal.

See also

Maximal Element, Partial Order, Partially Ordered Set

This entry contributed by Jay S. Nakahara

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Jech, T. J. Set Theory, 2nd ed. Berlin: Springer-Verlag, 1997.

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Comparable Elements

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Nakahara, Jay S. "Comparable Elements." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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