Is it true that the cardinality of a hypothesis class with finite VC dimension is less than the cardinality of real numbers?
My intuition is that the number of functions in a hypothesis class with finite VC dimension cannot grow arbitrarily and there is a limit on that.
For any set $X$, the hypothesis class $\{\{x\}\mid x\in X\}$ consisting of singletons has VC-dimension $1$ but cardinality $|X|$. So there is no bound on the cardinality of a hypothesis class depending on the VC-dimension.