From Appendix B.2 (relations) of Introduction to Algorithms by Cormen et al:
In a partially ordered set A, there may be no single "maximum" element a such that b R a for all b ∈ A. Instead, there may several maximal elements a such that for no b ∈ A, where b ≠ a, is it the case that a R b. For example, in a collection of different-sized boxes there may be several maximal boxes that don't fit inside any other box, yet no single "maximum" box into which any other box will fit.
I know the definition of a partial ordered set , but do not get why the author/authors say that "there may be no single "maximum" element" in a partially ordered set ?