Final answer:
A finite point set will always have a first point and a last point.
Step-by-step explanation:
To prove that a finite point set has a first point and a last point, we can use the concept of ordering. Let's assume that M is a finite point set. We can define an ordering on M based on the distances between the points. For any two points p and q in M, we can say that p comes before q if the distance from the first point in M to p is less than the distance from the first point in M to q.
Using this ordering, we can see that the first point in M is the minimum element in the ordered set, since it has the smallest distance to the first point in M. Similarly, the last point in M is the maximum element in the ordered set, since it has the largest distance to the first point in M.
Therefore, based on this ordering, a finite point set M will always have a first point and a last point.