Distance axiom: Distance is symmetric, positive definite, and satisfies the triangle inequality.

Distance is a function which assigns, to every ordered pair of points (A,B), a real number d(A,B).

Distance axiom

1. Symmetry: For all A, B, d(A,B) = d(B,A).

2. Positive definiteness: For all A, B, d(A,B) ≥ 0, and d(A,B) = 0 if and only if A = B.

3. Triangle inequality: For all A, B, C, d(A,B) ≤ d(A,C) + d(C,B).

Definition: If A is a point and r is a positive real number, the circle with center A and radius r is the set of all points B such that d(A,B) = r.

C. McCrory 9/17/04