Proof that 1+1 = 2 【Fundamentals of Mathematics】

I think we've all had the question (at least once) on why 1+1=2. It's like asking the definition of 'the', and it's rather confusing on whether this is even an approachable idea. So, I made this video to share a very simple proof.

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Timestamps:

00:00 Why I'm making this video
01:11 Introduction
01:51 Defining Equality
03:19 Defining Natural Numbers
07:20 Defining Addition
08:58 Proving 1+1 = 2
10:27 Key Takeaways
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This is my first time I've decided to edit videos. The journey started about a week or two weeks ago where I decided that this would be a good learning opportunity. And, though I'm not extremely strong in the field of math, I though this was something that we all miss out on, even though understanding the theory and method is extremely simple. And if I'm perfectly honest, I don't think there are too many videos explaining the fundamental ideas on why 1+1 really equals 2, but more videos on 1=2, 1+1=3, or along the lines which is a bit sad. As I mention in the video, Math is based on axioms, and so, we should spend a little more time understanding what kinds of axioms shape the math that we use today. If you are reading this, thank you for watching, and I hope you enjoy (or enjoyed) !

So, I actually tried to dumb down the words as much as I could in this video, meaning I decided not to mention some few things. And so I'll write about it here.

This proof is based on a set of axioms commonly referred to as the Peano Axioms (I'm not really sure how to pronounce this), and was made in the 19th century by Peano.

The proof is really simple if you watch it; there's no hard ideas, and probably the hardest part of this video is me repeatedly saying successor. Other than that, it's simple ideas we all know are true, but if you think about it, these are the only things you need to know to prove 1+1=2.


#3b1b #SoME1

Music Credits:
Quaternions · Vincent Rubinetti
   • Quaternions  
Resonance · Vincent Rubinetti
   • Resonance  

Thank you to 3b1b, all of the discord and reddit support, and brillant for making this project be an enjoyable few weeks spend over the summer.