B1) If B is between A and C, (written A*B*C), then A, B, C are three distinct points on a line, and also C*B*A.

B2) For any two distinct points A, B, there exists a point C such that A*B*C

B3) Given three distinct points on a line, one and only one of them is between the other two.

B4) Let A, B, C be three non-collinear points, and let

be a line not containing any of A,B,C. If

contains a point D lying between A and B, then it must also contain either point lying between A and C or a point lying between B and C, but not both.

As for

, the '+' here is the field addition and

.