The Principle of Strong Mathematical Induction
 Principle of Strong Mathematical Induction: Let $n_0 \in \mathbb{N}$ and let $P(n)$ be a statement relevant to all natural numbers $n ≥ n_0$. If the statements $P(n_0)$ is true and the truth of $P(n_0), P(n_0 +1), P(n_0 + 2), ..., P(k -1), P(k)$ implies the truth of $P(k+1)$, then $P(n)$ is true for all $n ≥ n_0$.