*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:*

#### Part 1 - Natural Numbers (in Set Theory)

**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**.

#### Part 2 - Natural Numbers (Successor Map and Addition)

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

#### Part 3 - Natural Numbers (Induction and Associativity

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

#### Part 4 - Natural Numbers (Ordering)

Let us talk about the **ordering** the natural numbers have:

#### Part 5 - Natural Numbers (Multiplication)

The next operation for the natural numbers is the **multiplication**:

#### Part 6 - Integers (Construction)

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

#### Part 7 - Integers (Addition and Inverses)

What are the important **properties** of the **integers**?

#### Part 8 - Integers (Multiplication)

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

#### Part 9 - Rational Numbers (Construction)

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

#### Part 10 - Rational Numbers (Addition and Multiplication)

The rational numbers form a so-called **field**:

#### Part 11 - Rational Numbers (Ordering)

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

#### Summary of the course Start Learning Numbers

- You can download the whole PDF here and the whole dark PDF.
- You can download the whole printable PDF here.