Footnote 2.5.

Technically, strong induction does not require you to prove a separate base case. This is because when proving the inductive case, you must show that \(P(0)\) is true, assuming \(P(k)\) is true for all \(k \lt 0\text{.}\) But this is not any help so you end up proving \(P(0)\) anyway. To be on the safe side, we will always include the base case separately.
in-context