Interesting but there is something weird about this analysis b/c they seem to assume a discrete input space & a continuous output space of uncountable cardinality whereas the input space is necessarily finite dimensional (in the continuous case) & of finite cardinality in the discrete case. It would be more interesting if the analysis actually used finiteness of the output space b/c real numbers are an idealization & in theory it is possible to injectively embed any discrete set into the real numbers simply b/c of the logic of cardinal arithmetic.