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
Resonance · Vincent Rubinetti

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.

[CannedMaths]

I've noticed a few word choices or errors that makes the statements confusing or incorrect so I'll put them here:

4:26 When I say #2 is false for 0, it would mean 0 has no successor (It does: it's 1). Rather, I should have phrased it that no number's successor is 0. I hope this is clear with the explanations thereafter.
5:38 -successor- predecessor
6:19 It should have said that if 0 has some property, and if a having with that property implies S(a) also has that property, all natural numbers have that property.

Sorry for these errors I hope you don't get confused by it.

If you are here as part of the SoME1 peer review, thank you so much for taking your time to watch this video.
If anyone is really low on time, you can skip to 8:58 or 11:11 where I prove, and give a conclusion on the video!

Thank you so much for watching!

[Solrex_the_Sun_King]

When you go back to level 1 to do it in expert mode.

[bigfloppalover]

Thanks man this finally helped me get out of first grade; I've been stuck there for like 10 years now lol

[gonsoku]

"1+1=2"
"But how do we prove that?"
"Thats the neat part, You don't"

[edgeman]

Thanks mate my child had some trouble keeping up in their maths classes, this video has helped them a lot. Could you make another video proving that 1+2 = 3 soon?

[darkkupo]

I like the use of the equal sign to explain how an equal sign works

[Fogmeister]

This reminds me of the quote from Carl Sagan…

“If you wish to make an apple pie from scratch, you must first invent the universe”

[MaximQuantum]

The lecture: Proof for 1+1=2
The homework: Prove that 7+13=20
The brain teaser in the book: Prove that 3-2=1
The test: Prove that 3*4=12
*The exam: Prove the Collatz conjecture using only successors, 0 and 1.*

[kleinsalescopygeek]

POV: *It's your first day of Calculus class when the Math professor ask you to answer 1+1 plus with elaborate and concise explanation*

[aetheriox]

i always love how complicated proofs for basic arithmetic is.

[thedigitalodyssey]

Thanks for this video! I was so confused when my kindergarten teacher said 1+1=2. I had no idea what it meant, but now I finally understand.

[scrungozeclown]

Now prove that 3 blues is approximately 1 brown

[TheIndieGhost]

thought this was a shitpost.

It was not a shitpost.

[LucasDenhof]

When you finished a game and go to the starting area with all your op gear

[nickcunningham]

I always wondered how you could prove that 1 + 1 = 2 because that in of itself always seemed so fundamental to me. I mean, like you said, it's the first thing ever taught when kids are first learning math. I could not comprehend how the hell you could get any more basic until I watched this video. Thank you

[schizoframia]

3:24 “we need to define natural numbers. NUMBER ONE” 💀💀💀💀

[coocooman]

As a physics major, I sometimes think mathematicians overthink things.

[ethanlynch]

great explanation! im about to finishe my undergrad in mathematics and i've never really dove this far into things. good stuff, keep it up!

[Wecoc]

I always thought this was one of those topics that required either 2 seconds or +10 hours of discuss with no inbetweens, this video is almost a miracle.

[Ali_Alhakeem]

This feels like going back to play the Tutorial after finishing the Game