Hi, I am just working on random problems to study for my midterm, but then I came across this one I don't know how to do. Plz help me. Thankkk youuu sooo much.
1) Suppose that A, B, C are collinear points in R^3 whose coordinates are given by (a1, a2, a3), (b1, b2, b3), and (c1, c2, c3) respectively. Prove that A*B*C holds if we have a1 < b1 < c1, a2 = b2 = c2, and a3 > b3 > c3.
Well, TPH this question may be beyond your experience.
In any metric space ‘betweeness” is a well-defined concept.
A*B*C means that d(A,B)+d(B,C)=d(A,C).
Hilbert’s axioms are for a synthetic geometry.
This question is not about synthetic geometry.
In traditional mathematics, is not synthetic geometry.