# Is the VC dimension of a set of classifiers bounded by the input space its defined on?

whats the relation between an input space and the VC dimension of a family of classifers on that space?

as in, if H is the set of classifers, and H is defined on a really small input space (say A = {1, 2}), then is VC(H) bounded by the size of the input space?

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