Mathematical Induction is a special way of proving things. Mathematical induction is a method of mathematical proof typically used to establish a given statement for all natural numbers. Explain why induction is the right thing to do and roughly why the inductive case will work.
The induction axiom in Peano Arithmetic says that for any predicate statement about numbers ϕ if you can prove ϕ 0 is true and you can also prove that for any number n ϕ n ϕ n 1 then ϕ n is true for all n.
Go through the first two of your three steps. Step 2 Inductive step It proves that if the statement is true for the n th iteration or number n then it is also. When you are asked to prove a statement by mathematical induction you should first think about why the statement is true using inductive reasoning. Then the integer 1 belongs to F since 1 1 2.