Actual Proof 1+1=2

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This video presents a clear and concise proof of why 1+1 equals 2, a fundamental concept in mathematics. It breaks down the logic and reasoning behind this basic equation, making it understandable for anyone interested in math.

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Disclaimer: This video is for entertainment purposes only and should not be considered academic. Though all information is provided in good faith, no warranty of any kind, expressed or implied, is made with regards to the accuracy, validity, reliability, consistency, adequacy, or completeness of this information. Viewers should always verify the information provided in this video by consulting other reliable sources.

[BriTheMathGuy]

🎓Become a Math Master With My Intro To Proofs Course! (FREE ON YOUTUBE)

[maxhagenauer]

That hit hard when he said "If you really want to up your math game..." at the end of the video where he explains why 1 + 1 = 2.

[Vakummraleee]

This is what the teacher expects you to do when they say "show your work"

[GlorifiedTruth]

I have spent the last 40 years of my life trying to disprove this postulate. I graciously accept defeat at your hands, sir. SIGH.

[Gelster]

This is the math equivalent of having to meet the minimum 1000-word count in your essay

[weo]

Meanwhile john hush proving 1=2 in every single way possible 🗿

[throughthoroughthought]

My Second-grader says "nu-uh." And I can't disagree with them.

[gheffz]

This "logic" proof could be written in a computer language called Prolog:

_% Base case: Adding 0 to any number N results in N._
plus(0, N, N).

_% Recursive case: To add A and the successor of B, we first add A and B, then find the successor of the result._
plus(s(A), B, s(C)) :- plus(A, B, C).

?- plus(s(0), s(0), s(s(0))).

[davidmadar]

The name of the video is miseading, in my opinion. This is not really a proof that 1+1=2, but a proof that the definition of addition presented here is consistent with the result "1+1=2". If it wasn't consistent, the conclusion had not been that 1+1 does not equal 2, but that our definition for addition is faulty. This kind of proof put the result as something we want to achieve, because we assume it is true intuitively but lack the formal tools to describe it: we try to build a system of axioms and definitions that will lead to the result we wanted it to lead, and than we prove we succeded. Therefore it is meaningless to say we "proved that 1+1=2". What we did was finding an extremely elegant definition for addition that is consistent with the intuitive idea we already had and just wanted a formal set of axioms that will lead to it. This definition, or an extension of it, might become interesting and useful when it comes to adding things we don't have intuition about, such as infinity.

[jacob_s]

It is interesting how often in science and math the most tangible things are often the hardest to define in abstract terms.

[Laicicles]

1:40 how can we use addition to define addition? How can that make sense?

[Bodyknock]

0 is very often included as a Natural Number when you are using set theory as the underlying basis since the Naturals are then defined as being the set of all possible finite cardinalities, and since the cardinality of the Empty Set is 0 that makes it a Natural Number.

Where 0 isn’t usually included as a Natural Number is when you’re working in Number Theory since 0 is an annoying exception in a lot of theorems involving factorization. It’s simply more convenient to define the Naturals as starting at 1 in that context so you don’t have to keep dealing with 0 as a special case.

[TheLuckySpades]

So 0 or 1 being the initial natural is actually a big split in conventions, in ny experience German speaking areas were more likely to start with 1, French and English speaking with 0, though English was the most mixed of the bunch

And this split goes back even before Peano pubished his formalization, he was actually beaten to the punch by Dedekind (his formalization is equivalent, but also harder to state and closer to second order logic than first order)
In Dedekind's initial manuscripts he started at 0, but somewhere in the process he began starting it at 1, he never wrote down why he changed it, but if I were to guess, the way he was approaching proofs became more elegant and simpler to write after the change, others went with 0 because their approaches had the opposite side for elegance

[PeacemakerD]

Wish these videos were out 12 years ago. Been wishing for an understandable explanation since high school, thank you so much!!!

[zyphre]

You define addition with addition?? how is that proof bruh.

[PeacemakerD]

Can you explain the set theory behind the definition of addition?

[кирофф]

0:20 at this point the 2 circles and the loading icon came together perfectly lol
upd: maybe only in my phone

[revtheobbyist]

"you 'probably' agree with me"

[tombaron]

Yes but can you prove that 6 was in fact scared of 7?

[averagenpc]

somehow I always feel like there's a sentence missing in that proof where we have decided that the successor of 1 should be 2, written like that and pronounced as "two". you get what I mean? I feel like it should be mentioned somewhere that the label of the thing was defined as well, and that it is two (2). otherwise, the proof just leads me to 1+1=S(1) and the question of "ya but why is that 2?" is still there.