A little puzzle

[Elroch]

On reflection, it makes more sense to prove the slightly stronger result when you pick N points randomly (with uniform distribution) from the the first M points. i.e. by picking M big enough, you can ensure the probability of the points not being shattered is as small as you wish.

[Michael Reach]

I hear you; good point. I note that there is an problem in Chapter 2 that reminds me of this one. (I don't have the book in front of me but it uses the "floor" function of an exponent.)