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There is a set called X; X = { 2, 5, 15, 40, 120, 111, 140 } And I drew the divisibility hasse diagram of this set. enter image description here

I know 120 and 140 are maximals, 2 and 5 are minimals, minimum and maximum dont exist. But I am not sure about is 111 maximal or minimal or both. Because 111 fulfill the definitions of maximal and minimal at the same time.

Asaf Karagila
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ceyhunmelek
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    In this poset, $111$ is both maximal and minimal. It satisfies both definitions, as you recognized. – amrsa Dec 20 '17 at 14:14

1 Answers1

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As you note the number $111$ fulfills both definitions, and hence it is both minimal and maximal.

Servaes
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