Moulton Plane - Formal Definition

Formal Definition

The Moulton plane is an incidence structure, where denotes the set of points, the set of lines and the incidence relation "lies on":

is just a formal symbol for an element . It is used to describe vertical lines, which you may think of as lines with an infinitely large slope.

The incidence relation is defined as follows:

For p = (x, y) ∈ P and g = (m, b) ∈ G we have

p\,\textrm I\,g\iff\begin{cases} x=b&\text{if }m=\infty\\ y=mx+b&\text{if }m\geq 0\\ y=mx+b&\text{if }m\leq 0, x\leq 0\\ y=2mx+b&\text{if }m\leq 0, x\geq 0. \end{cases}

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