A Tour of the Real Numbers

In this video we'll discuss what natural numbers, integers, rational and real numbers are and what properties these different numbers have.

Chapters:
0:00 - Introduction
2:18 - Natural Numbers
3:59 - Integers
4:29 - Rational Numbers
6:00 - Irrational Numbers
7:14 - Square root of 2 is irrational (proof by contradiction)
9:11 - Real Numbers

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As mentioned in the video:

Errata and Clarifications:
At 8:30, 2k/2l = k/l not 2(k/l) as shown.

The Maths Essentials series is based on the books:

This video was made using:
Animation - Apple Keynote
Editing - DaVinci Resolve

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Thank you so much, I hope you find the content useful.

[andy-kgfb]

This channel is Underrated!! One of the best maths channels I know out there.

[ClementinesmWTF]

I just found your channel and I’m absolutely loving it, visuals and all. I really appreciate the dedication to actual mathematical methods and theorems rather than applications in very particular problems and situations—3B1B is cool and all (really, no hate towards him), but his work feels a little too focused on things that can’t be as easily generalized and used in many other situations.

On a side note: I really hope you expand this video into a serialized thing exploring different kinds of numbers and their properties and uses (maybe add in some subcategories of algebraic numbers within the reals, imaginary and complex numbers, quadratic integers; show how there is an infinite—yet decreasingly useful—family of hyperreals and how they relate to vectors, matrices, and generalized tensor families). I’m really hoping this channel blows up with subscribers like it deserves to!

[TimothyShevgun]

Hello! Nice video!
However, you made a mistake at 8:30. "2" is the common multiplier of both numerator and denominator of that fraction. You could not write it as the multiplier before the fraction.

[innidynamics]

Hi, I'm student from Indonesia..
thank you for the explanation. this help me a lot.
I hope your channel continues to grow

[venkataramayya]

How about "Category Theory" as a part of the Math Essentials?

[rickdoesmath]

1:44 you confused linear orders with well orders here

[keloglan]

What about division by 0? It seems to me that the reals or rational numbers should not be closed under division due to the problem of division by 0?

[stopstopp]

Real Numbers are not closed under division, because dividing by zero leads to undefined. An answer that is undefined is not a real number.

[jaytravis]

I was amazed when i realized that the set of 'DEFINABLE NUMBERS' is SMALLER than the set of ALL NUMBERs. ...and im sure if you mull over that a bit you will shortly enounter a contradiction

[edmundwoolliams]

At the end I was hoping for:

“But the real numbers belong to an even larger set...

...called the *octonians*”

[alejandrobarrantes]

natural number and integral numbers have the same amount of numbers like Q too, using Venn diagrams to represent them gives generally the wrong notion that N has less cardinality than Z ...😵😓

[MB-orkh]

Where did the "l" come from in b = 2l ?