Show solution Note that our description of Hasse diagrams made use of the covers relation \. The covers relation, however, is not a helpful in many posets\. Consider the poset of the real numbers ordered by the standard comparison \. We have , but how would we convey that with a Hasse diagram? The problem is that has no covers, even though it is not a maximal element in \. In fact, for any such that , we can find a such that \. This "infinite density" of makes it impossible to depict using a Hasse diagram\.
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