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We prove that, for any $d$ linearly independent functions from some set intoa $d$-dimensional vector space over any field, the family of zero sets of allnon-trivial linear combination of these functions has VC-dimension andLittlestone dimension $d-1$. Additionally, we characterize when such familiesare maximal of VC-dimension $d-1$ and give a sufficient condition for when theyare maximal of Littlestone dimension $d-1$.

Littlestone and VC-dimension of families of zero sets