VC-dimension of Hyper-rectangles

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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?