Show that a hyperplane can split n points in at most (n+ 1)d+1 different ways. Hint: Use Theorems 9.3 and 9.5 to bound the shatter coefficient of the set                           A = x ∈ Rd : a1x(1)...

Show that a hyperplane can split n points in at most (n+ 1)d+1 different ways.

Hint: Use Theorems 9.3 and 9.5 to bound the shatter coefficient of the set

                          A = x ∈ Rd : a1x(1) + ··· + adx(d) + ad+1 ≥ 0 : a1,...,ad+1 ∈ R .