induction

This page will use a small amount of information from the chapter on Set Theory. It is not required, but understanding sets might be helpful to get how induction works.

Smallest Numbers Consider the natural numbers $\mathbb{N}$, what is the smallest number? Clearly the answer is $0$, as it is smaller than every positive number, and there are no negative numbers in $\mathbb{N}$ so it must have $0$ as the smallest.