# 10+ Hasse Diagram Greatest And Least Element Background

10+ Hasse Diagram Greatest And Least Element
Background
. The least upper bound and the greatest lower bound do not always exist. The greatest and least elements are unique when they exist. Special Elements Of Partially Ordered Sets from www.math24.net A hasse diagram is a graphical representation of a partially ordered set. So, how we construct the hasse diagram of18:07the poset poset x less than equal to, where x is 1, 2, 3, 4, because earlier we have shown18:23that for this relation are less than equal to it is a poset. In a hasse diagram, a vertex corresponds to the greatest element if there is a downward path from this vertex to any other vertex.

### They are respectively note, however, that this example is quite special:

Is a partial order relation. Greatest element and least element: Transcribed image text from this question. In a hasse diagram, a vertex corresponds to the greatest element if there is a downward path from this vertex to any other vertex.