"Not clear what this means?"

https://arbital.com/p/5t8

by Eric Bruylant Aug 8 2016


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\.

Not clear what this means?