| 21. | This set has no greatest element, since for every element of the set, there is another, larger, element.
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| 22. | Any least element or greatest element of a poset is unique, but a poset can have several minimal or maximal elements.
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| 23. | The notion of greatest element for a preference preorder would be that of "'most preferred "'choice.
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| 24. | Bounded completeness has various relationships to other completeness properties, which are detailed in the article on least and a greatest element.
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| 25. | The greatest element in this fiber is the discrete topology on " X " while the least element is the indiscrete topology.
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| 26. | Of course, when the restriction of \ leq to S is a total order, the notions of maximal element and greatest element coincide.
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| 27. | One can define half-closed and closed intervals,, and by adjoining as a least element and / or as a greatest element.
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| 28. | But the notion of " eventually " applies to functions on more general sets, specifically those that have an ordering and no greatest element.
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| 29. | :I think you have confused maximal element with greatest element .-- talk ) 19 : 46, 20 February 2008 ( UTC)
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| 30. | Dually, the existence of an upper adjoint for " j " is equivalent to " X " having a greatest element.
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