Question

Betweenness of points anyone?

Answer 1

What do you mean?

Answer 2

Like, what do you need to solve or understand of this theorem?

Answer 3

Betweenness is the property of lines in certain geometries, which allows one to talk about when a third point is between two points.
Betweenness is equivalent to the line being a linear order of its points.

The Betweenness of Points Theorem states that:
A point is between two other points on the same line iff its
coordinate is between their coordinates.
If A-B-C, then AB + BC = AC.
The notation A-B-C means that A, B, and C are points on a line, and B
is between A and C.
In other words, it looks like

<-------------+-----+-------------+------->
A B C

Betweenness Theorem says that whenever B is between A and C,
you can add the distances AB and BC to get the distance AC:

AC
|<----------------->|
AB BC
|<--->|<----------->|
<-------------+-----+-------------+------->
A B C

If B were NOT between A and C, you couldn't do that.