"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 prec\. The covers relation, however, is not a helpful in many posets\. Consider the poset langlemathbbR,leqrangle of the real numbers ordered by the standard comparison leq\. We have 0<1, but how would we convey that with a Hasse diagram? The problem is that 0 has no covers, even though it is not a maximal element in mathbbR\. In fact, for any xinmathbbR such that x>0, we can find a yinmathbbR such that 0<y<x\. This "infinite density" of mathbbR makes it impossible to depict using a Hasse diagram\.

Not clear what this means?