Hasse Diagram Divisibility. Concretely for a partially ordered set 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. If the number 1 is excluded while keeping divisibility as ordering on the elements greater than 1 then the resulting poset does not have a least element but any prime number is a minimal element for it.
Since a partial order is reflexive hence each vertex of a must be related to itself so the edges from a vertex to itself are deleted in hasse diagram. The resulting graph looks far simpler and is called a hasse diagram named after the german mathematician helmut hasse 1898 1979. How would you draw a hasse diagram of the divisibility relation.
In above diagram 3 and 4 are at same level because they are not related to each other and they are smaller than other elements in the set.
So 1 will be connected to each other element. A hasse diagram is a graphical representation of a partially ordered set poset. 2 3 5 1. Fig 1 helmut hasse 1898 1979 as an example consider the divisibility relation a b on the set.
