In this post, I will write about three kinds of inductions: weak induction, strong induction, and structural induction. I in fact dislike these terms because, as I will show below, they are equivalent. Personally, when I think of induction, I will default to the structural induction. Last semester I took a logic class, and they introduce these terms, and also “formula induction”, “proof induction”, “term induction”, “sequence induction”, etc. I was like: *sigh* THEY ARE THE SAME WHY DO YOU NEED DIFFERENT NAMES.

Anyway, for the sake of this article, we will do use these terms for clarity and show the following.