I have question about VC-dimension(Hyper-rectangles in Rn) = 2n
Hyper-rectangle = [a1,b1]×[a2,b2]×⋯×[an,bn]
I trying to prove that the VC-dimension for Hyper-rectangles of size n in Rn dimension, is 2d.
I trying to do with induction , but I not able to do it.
base case: n = 1 or n = 2, for line(d=1), we can take to point in each interval, means VC-dimension = 2 same for rectangle in R2, VC-dimension =4.
I will assume that this is true for n-1.
but how I can do it for n dimension?