# Start Learning Numbers

Here, you find my whole video series about Start Learning Numbers in the correct order and I also help you with some text around the videos. If you have any questions, you can use the comments below and ask anything. However, without further ado let’s start:

### Introduction

Start Learning Numbers is a video series I started for everyone who is interested in the necessary foundations you need to enjoy the whole world of mathematics. Now by knowing the basics in set theory, we are able to construct of known mathematics just out of sets. This makes everything stands on solid grounds. We start with the natural numbers.

### Let’s get started

The natural numbers have a recursive property one can use for definitions:

The whole concept leads the mathematical induction, which helps a lot in proofs:

Let us talk about the ordering the natural numbers have:

The next operation for the natural numbers is the multiplication:

Having all these things, we can start talking about the integers. Let us construct them using pairs of natural numbers:

What are the important properties of the integers?

The integers also need a multiplication which we can define using the already known multiplication of natural numbers:

Next on our list of number sets we want to construct are the fractions, the rational numbers:

The rational numbers form a so-called field:

The only thing that we have to add to rational numbers now is an ordering, which conserves the ordering from the other number sets: