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}

Read more about this topic:  Moulton Plane

Famous quotes containing the words formal and/or definition:

    “The formal Washington dinner party has all the spontaneity of a Japanese imperial funeral.”
    —Simon Hoggart (b. 1946)

    “Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
    —Elaine Heffner (20th century)