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.


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Let’s get started

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


Watch Start Learning Numbers Part 2 PDF Version Quiz


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


Watch Start Learning Numbers Part 3 PDF Version Quiz


Let us talk about the ordering the natural numbers have:


Watch Start Learning Numbers Part 4 PDF Version Quiz


The next operation for the natural numbers is the multiplication:


Watch Start Learning Numbers Part 5 PDF Version Quiz


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


Watch Start Learning Numbers Part 6 PDF Version Quiz


What are the important properties of the integers?


Watch Start Learning Numbers Part 7 PDF Version Quiz


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


Watch Start Learning Numbers Part 8 PDF Version Quiz


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


Watch Start Learning Numbers Part 9 PDF Version Quiz


The rational numbers form a so-called field:


Watch Start Learning Numbers Part 10 PDF Version Quiz


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


Watch Start Learning Numbers Part 11 PDF Version Quiz


Go to the next course

Start Learning Logic
Start Learning Sets
Start Learning Numbers
Start Learning Reals
Start Learning Complex