I'm confused about why this proposition is true if this property is not true at all.
$Proposition$ 2.1.11.
A certain property $P(n)$ is true for every natural number n.
Proof. We use induction. We first verify the base case $n = 0$, i.e., we prove $P (0)$. (Insert proof of $P (0)$ here). Now suppose inductively that n is a natural number, and $P(n)$ has already been proven. We now prove $P$(n++). (Insert proof of $P(n++)$, assuming that $P(n)$ is true, here). This closes the induction, and thus $P(n)$ is true for all numbers n.
Thanks.