On 26 Apr 2001 08:54:44 -0400, firstname.lastname@example.org (Mike Schubert) wrote:
>How it can be proved that for n>=3, n distinct points in the plane, >not all on a single line, determine at least n distinct lines ?
Sounds like a natural for induction, with a little twist. Work it out for n=3. Then try n=4.
The twist is that for general n, it seems to me you have to take two different cases: (1) n-1 points are colinear, and you are adding one more, or (2) there are no sets of n-1 points which are colinear, in which case the induction hypothesis holds.