I need to prove the Theorem: If omega is equal to infinity then D =[0,infinity) and if omega<infinity, then D =[o,infinity]. Where omega=the least upper bound of D and D=the set of all distances that occur between points of the plane. I'm really just not sure where to start, but I'm pretty sure it uses the following axioms: *For any point (A) on a line (m), there exists a point (B) on (m) with 0<AB<omega. and *For any ray AB and any real number s with 0< s< omega, there is a point X in the ray AB with AX=s. Any help would be great. Thanks!