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A Hasse diagram draws a finite partially ordered set using one point for each element and an upward line from $x$ to $y$ for each cover relation $x\prec y$. It omits reflexive loops and comparisons already implied by paths. Line crossings are not additional elements. In a finite partially ordered set, following upward paths recovers exactly the original comparisons. The diagram is named after Helmut Hasse.

A mathematician specializing in algebraic number theory. The Hasse diagram is named after him.^[ref][ref]

The prime numbers $2,3,5$ form the lower antichain; the nonprime elements $1,4$ form the upper antichain. In particular, $1$ is not a prime number. Each lower element is below each upper element, and no third element can lie strictly between them. Therefore the six cover relations are $2,3,5\prec 1,4$, represented by the following Hasse diagram. Upward movement represents increasing order; crossing lines do not add elements.