- A dichotomy of a set $S$ is a partition of $S$ into two disjoint subsets.
- There are $2^{|S|}$ possible dichotomies in instance set $S$.
- A set of instances is shattered by hypothesis space $H$ if and only if for every dichotomy of $S$ there exists some hypothesis in $H$ consistent with this dichotomy.
- The ability of $H$ to shatter a set of instances is a measure of its capacity to represent target concepts over them.