A (family of) proof method(s)

Simple Induction

To prove a statement $\forall n \in \mathbb{N}, P(n)$ by induction, you need:

• Base case: proving that the statement is true for the first natural number $n=0$.
• Inductive step: $$ \forall k \in \mathbb{N}, P(k) \implies P(k+1) $$