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The above orders are all very common in mathematics. However, there are also examples that one does often not consider as orders. For instance, the identity relation = on any set is a partial order. Within this order, every two elements are incomparable. It is also the only relation that is both a partial order and an [[equivalence relation]]. The Hasse diagram of such a '''discrete order''' is just a collection of labeled points, without any edges between them.
Another example is given by the divisibility relation "|". For two natural numbers ''n'' and ''m'', we write ''n''|''m'' if ''n'' [[division (mathematics)|divides]] ''m'' without rest. One easily sees that this really yields a partial order. An instructive exercise is to draw the Hasse diagram for the set of natural numbers that are smaller than or equal to 13, ordered by |.
=== Special elements within an order ===
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