Techniques of proof IV: Induction
One thing leads to another.
Induction is a very powerful technique used regularly by mathematicians.1 Initially, it can be confusing because it looks like we assume what is to be proved. As we know, that never proves theorems. On the plus side, spotting when to use it is easy and we need only check two conditions to apply it.
Induction is applied when we have an infinite number of statements indexed by the natural numbers such as
‘n5 − n is even for all n ’.
It is not sufficient to prove this ...