Hasse diagram

Summary

A Hasse diagram is a drawing of a finite partially ordered set. Each element is a point, and there is a line upward from $a$ to $b$ when $b$ covers $a$. This means that $a < b$ and no $c$ satisfies $a < c < b$. Then $a \le b$ exactly when one can go from $a$ to $b$ by a path that goes only upward.

Remarks

The diagram does not draw the loops of reflexivity or the lines that transitivity implies. The Hasse diagram of the power set of $\{1, 2, 3\}$ under $\subseteq$ is the picture of a cube.

Explanations

L1 human

A Hasse diagram is a minimal picture of an order. For the divisors of $12$ under divisibility, put $1$ at the bottom and $12$ at the top. Draw a line from $2$ to $4$ and from $2$ to $6$. Do not draw a line from $2$ to $12$, because the path through $4$ already shows it.