*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:

### Go to the next course

Start Learning Logic

Start Learning Sets

Start Learning Numbers

Start Learning Reals

Start Learning Complex