 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-1/31k/a/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

For points

z_{1}, l d o t s, z_{n}

, let

H (z_{1 : n}) = {(h (z_{1}), \dots, h (z_{n})) : h \in H} .

s (H, n) = sup_{z_{1 : n}} ∣ H (z_{1 : n}) ∣, V C (H) = sup {n : s (H, n) = 2^{n}} .

Thus a set of $n$ points is shattered when every binary labeling occurs on it.

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