| 1. | Like upper bounds, greatest elements may fail to exist.
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| 2. | A set can have several maximal elements without having a greatest element.
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| 3. | This set has a supremum but no greatest element.
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| 4. | In other words, m is a greatest element.
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| 5. | An order that has both a least and a greatest element is bounded.
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| 6. | Partially ordered sets without greatest element or maximal elements admit disjoint cofinal subsets.
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| 7. | Potlatch showcases two of the greatest elements of ultimate, competition and sportsmanship.
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| 8. | We begin by showing that " P " has least and greatest element.
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| 9. | The pseudo-complement is the greatest element " y " such that.
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| 10. | The existence of least and greatest elements is a special completeness property of a partial order.
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