Question

Need a proof for: If l is any line, then there exists at least one point P such that P does not lie on l.

Answer 1

Using the incidence geometry axioms
1. for every pair of distinct points P and Q there exists exactly one line such that both P and Q lie on l.
2. For every line l there exist at least two distinct points P and Q such that both P and Q lie on l.
3. There exist three points that do not all lie on any one line.