HW1: Prove that for all k there is a large enough N such that for n>=N points on the plane, either there is a subset of k points on a line or a subset of k points in general position.
HW2: show both conditions of the silva fukuda conjecture are necessary, i.e, 1) there exist (arbitrarily large) point sets consisting of red and blue points such that the red and blue are separable by a line and there does not exist a bichromatic line 2) there exist (arbitrarily large) point sets consisting of red and blue points such that the cardinality of red and blue differ by at most 1 and there does not exist a bichromatic line. (for all statements above, both the red and blue point sets are non empty)