The Principle of Strong Mathematical Induction

The Principle of Strong Mathematical Induction

Be sure to read on The Principle of Weak Mathematical Induction before reading forward.

We will now look at the technique of proving certain statements by what is known as strong induction. The idea is practically the same with the exception of starting off with a "stronger" hypothesis in a sense.

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 $n ≥ n_0$.
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