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i want to know some examples of supremum or infimum on a poset using relation, other than $\le$, for example using divides or mod. basiclly i want to know how to find out the supremum of a poset for an arbitary relation.

thank you

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hari
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    For an arbitrary partial order, we can hardly say more than: use the definition. The infimum with respect to "divides" is (of course) the gcd – Hagen von Eitzen Jan 22 '14 at 15:56

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