More Bases for Strong Induction - Supersedes Weak Induction? I recently learned about strong induction, and had a couple questions. First, on sites such as this one: http://www.mathblog.dk/strong-induction/ , it is said that using strong induction requires more bases case. (This makes sense to me, as you are making a bigger claim) When I asked my professor, though, he said there are no more base cases needed. In this light, I don't see why anyone would ever go through the effort of even attempting 'weak' induction, as it is included in strong induction, and no extra steps of work are needed-only a larger assumption.

Strong induction is the following:


*

*Show that $p_0$ is true.

*Suppose that $p_1$, $\ldots$, $p_n$ is true and show that $p_{n+1}$ is true.

*Conclude that $p_i$ is true for all $i$


Weak induction is the following:


*

*Show that $p_0$ is true.

*Suppose that $p_n$ is true and show that $p_{n+1}$ is true.

*Conclude that $p_i$ is true for all $i$


Usually, it is considered more elegant to assume the least amount of things possible. So if you can finish your work by using only weak induction, it is preferred. As you pointed out, you could use strong induction instead of weak induction all the time.
