# VC Dimension of A Set of Hypothesis

I am confused about what does a VC dimension of a set of hypothesis means.

I have two hypothesis, say $H_1$ with VC dimension of $x$, and $H_2$ of VC dimension of $y$. Does this automatically mean that the VC dimension of this set is $max(x,y)$?

Or does this mean that I can use the combination of these two somehow to get a VC dimension which is possibly higher than $max(x,y)$? like if $H_1$ can't classify a specific ${(+,-)}$ combination of points but $H_2$ can classify it and vice versa, then that larger set is the new dimension of the set of hypothesis?

• VC dimension is a property of a set of hypotheses. It's not defined for a single hypothesis. The VC dimension of a set consisting of a single hypothesis is 0. – Yuval Filmus Jun 23 '18 at 20:06
• Perhaps you are interested in the VC dimension of a union of two sets? – Yuval Filmus Jun 23 '18 at 20:06