| 21. | Similar conclusions hold for least elements.
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| 22. | Complete lattices and orders with a least element ( the " empty supremum " ) provide further examples.
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| 23. | Every recursively enumerable ( or even hyperarithmetic ) nonempty subset of this total ordering has a least element.
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| 24. | Equivalently, one may define an atom to be an element that is covers the least element "'0 " '.
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| 25. | As defined in set theory, the maximum and minimum of a greatest and least elements in the set, respectively.
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| 26. | Dcpos with a least element ( " pointed dcpos " ) are called complete partial order ( cpo ).
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| 27. | The College Logo combines the Logos of St . Brendan s and Shaw Colleges, or at least elements from each.
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| 28. | By definition, this is the least element among all elements that are greater than each member of the empty set.
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| 29. | By the above reasoning the map exists and is unique since least elements of subsets of wellordered sets are unique.
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| 30. | In the case of topologies, the greatest element is the discrete topology and the least element is the trivial topology.
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