Peano Axioms: What are Natural Numbers?

Here we will look at how Natural Numbers where first defined in the 19th century. This will be done by exploring some of the basic Peano Axioms, better explained in this video. We will also prove a couple basic statements, using contradiction and induction.

If you have any comments, questions or suggestions, please let me know!

[math]

This channel in criminally underrated...Great video man! Looking forward for new video. I am new math student and this stuff is helpful. Thanks

ps. video idea: Archimedean axiom

[Rahul-yuro]

Amazing video thank you a lot, really like your way of teaching

[person]

At 2:47, could you please explain how you used the axiom 3 and why y=0?

[johannes]

Great video! Just the volume could be a bit louder. But otherwise very visual and helpful. Thanks a lot!

[raheem]

I would claim numbers are built from images

Example, 4 always represents 4 images, like 4 squares for instance.



1. The main idea here is that maths is built from images


(a) example, geometry is clearly made of images

b) example 2, We claim numbers are built from images too, as say 4, always represents 4 images, like 4 squares for instance.

C) imaginary numbers are connected to images too, which is why they have applications in physics

D) In general any mathematical symbol that comes to mind is connected to images too`

To be accurate numbers are "labels" for groups of images

[Bartuisacapybara]

Cool video bro subscribed can you make a video about trig functions and logarithmic functions

[shahedulalam]

0 is not a natural number.1 is the starting natural number.

[raheem]

I would claim numbers are built from images

Example, 4 always represents 4 images, like 4 squares for instance.



1. The main idea here is that maths is built from images


(a) example, geometry is clearly made of images

b) example 2, We claim numbers are built from images too, as say 4, always represents 4 images, like 4 squares for instance.

C) imaginary numbers are connected to images too, which is why they have applications in physics

D) In general any mathematical symbol that comes to mind is connected to images too`

To be accurate numbers are "labels" for groups of images