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  anchorContext: 'Show solution\n\nNote 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 $\\langle \\mathbb R, \\leq \\rangle$ 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 $\\mathbb R$\\. In fact, for any $x \\in \\mathbb R$ such that $x > 0$, we can find a $y \\in \\mathbb R$ such that $0 < y < x$\\. This "infinite density" of $\\mathbb R$ makes it impossible to depict using a Hasse diagram\\.\n\n',
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