From that link: “But what about when we want to describe physical quantities that have continuous values, such as the position of a particle along a line? In this case, we need a vector space of infinite and continuous dimension. Turns out that it’s possible to define a Hilbert space on the set of continuous functions, e.g., f (x) = x3 + 2x + 1. This is referred to as “wave mechanics” and we won’t cover it in this book.”