Hasse Diagram 4 Elements. Note however that this example is quite special. Is a type of mathematical diagram used to represent a finite partially ordered set in the form of a drawing of its transitive reduction concretely for a partially ordered set s one represents each element of s as a vertex in the plane and draws a line segment or curve that goes upward from x to y whenever y covers x that.
The hasse diagram of a finite poset is a useful tool for finding maximal and minimal elements. In order theory a hasse diagram ˈ h æ s ə. If the maximal or minimal element is unique it is called the greatest or least element of the poset respectively.
As many brackets are usually hard to understand the sets are defined by circles instead of brackets.
Let a be a poset a 2 4 6 8 and the relation a b is a divides b. The elements of v 4 respectively the subsets of v 3 ordered in a hasse diagram by inclusion. The hasse diagram of a finite poset is a useful tool for finding maximal and minimal elements. To draw the hasse diagram we start with the minimal element 1 at the bottom.
