O'Reilly logo

How to Think Like a Mathematician by Kevin Houston

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

CHAPTER 24

image

Techniques of proof IV: Induction

image

One thing leads to another.

Anon.

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

n5n is even for all n ’.

It is not sufficient to prove this ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required