Thank you, Mr Percent! I can finally mathematically prove that 1 = 7!

@electroencephaloctopus

Ай бұрын

Hate to break it to you, but 1 != 5040

@broor

Ай бұрын

I can prove that 6 = 3!

@netanelkomm5636

Ай бұрын

@@broorI can prove that 3!= 7

@FufuZ

Ай бұрын

Assume that the numbers 1 and 7 indicate a summation of vectors, whose starting and ending points are same in both summations. Using the vector theorem, if you start the vectors from the end point of the nose of the number 1 until its foot, you get the summed vector that looks more or less like this - _\_ Again, use vector theorem for the number 7 taking the direction starting from its nose to its foot. We see that the sum is _\_ Both are facing the same direction. If the nose of number 1 is tilted downwards, the length may not be the same between both 1 and 7. However if its straight maybe we can then say its equal. Here we proved that 1 = 7, or _\_ = _\_ , which also means 1 || 7.

@mz00956

Ай бұрын

​@@broor I approve of factorial

What you define as a "proof by contradiction" is typically known as a "proof by contra-positive", from formal logic if A -> B then it must also be true that ~B -> ~A. Usually a "proof by contradiction" is when we need to prove A->B so we assume (A wedge ~B) and reach a contradiction (a statement that is always false like (C wedge ~C), and thus A->B is proven.

@0prcent

Ай бұрын

Ah true, we did actually call this "proof by contra-positive" the same thing at uni but i see what you mean. But i guess then this negation of an implication is what i wanted to teach here anyways, just gave it a bit of a wrong name. Thanks for paying such close attention to detail!

@iamreallybadatphysicsbutda8198

Ай бұрын

@@0prcent No problem, I found you from your Jordan curve video, truly remarkable content

@ultimaxkom8728

Ай бұрын

@@0prcent _"How to prove anything"?_ Quite the ambitious thumbnail, though imo out of reach for the introduction. Good 3b1b animation is not a cure-all silver bullet, after all.

@ethanbottomley-mason8447

Ай бұрын

​@@ultimaxkom8728 The title is obviously hyperbole.

@ultimaxkom8728

Ай бұрын

@@ethanbottomley-mason8447 Yes, it's clickbait.

got a math olympiad tomorrow and somehow qualified without understanding proofs, but now i feel like im ready. thanks mate

Echoing other commenters, the "proof by contradiction" you showed is actually a "proof by contrapositive." That said, proof by contrapositive is often very helpful. I almost always start with some direct approach, and if that's too difficult, I'll look at the contrapositive. If I get lucky and the contrapositive is easier, I'll write that out, then rewrite it as a direct proof to make it look "cleaner." Aside: Something that's often overlooked is how much reading proofs improves your proof writing skills. I can't count how many problems I've solved by just applying the overall structure/approach someone else used.

there is some magical power in youtube algorithm which suggests me top tier quality mathematical video about topic which is relevant in school with no mistakes nor any delay

@0prcent

Ай бұрын

thank you so much!! (and thanks for the algorithm of course)

Thanks for explaining the "if and only if" part.

Can you prove the riemann hypothesis in a next video? Thanks!

@SlightSmile

Ай бұрын

Yeah this would be really helpful 🙏🙏

@tabiasgeehuman

Ай бұрын

​@@SlightSmile very would be an understatement

@deventerprises2640

Ай бұрын

Really helpful for my financial status

nice music choice

@user-sk4kg4hr3k

Ай бұрын

Baba is baba and not you

@turtleboy2150

Ай бұрын

Baba is win?@@user-sk4kg4hr3k

@walyssonbicoli385

Ай бұрын

@@user-sk4kg4hr3k now prove by contradiction (contra-positive)

wow, i really like your editing. the music choice, the graphics, the effects... very comfy. makes me want to study, even

@0prcent

Ай бұрын

aw thanks!

baba is you music is a perfect match for this subject

I never even had this introductuin in my course. Even though this is my second year doing computer science this was very helpfull. Thank you!

This is a very important video. I and many other people struggle with proofs. Thank you.

Really good video, thanks!

@0prcent

Ай бұрын

thank u

good video!, also i love the use of the va11halla OST :3

@0prcent

Ай бұрын

thx! so happy i got to use it in this video :)

@turtleboy2150

Ай бұрын

oooh that's what it is I was digging it the entire time

@0prcent

Ай бұрын

the full music list is also in the description btw if youre curious about any of the other songs

Thanks for covering this.

Incredible man, keep it up.

Great video. Starting my maths journey and this is very helpful

@0prcent

Ай бұрын

all the best!

first time I've heard _Baba is Me_ music in an unrelated youtube video

baba is logic

@totoroangelo0013

Ай бұрын

baba

@IzUrBoiKK

Ай бұрын

Les go you also recognised the bg music

this is such a good video. If this is what proofs are like then I definitely need to take more proof based math as part of my computer science degree.

@0prcent

Ай бұрын

im not sure how accurate my portrayal of the proofs are but if youre intrigued i can definitely recommend it, especially with analysis topics the approach tends to give you a much deeper understanding for whats actually going on

Today is my maths exam. Wish me luck!

@kamalkrishnabaral

Ай бұрын

I will bring 4 gpa.

@filipus098

Ай бұрын

good luck dude!

@kamalkrishnabaral

Ай бұрын

@@filipus098 thanks.

@paperclips1306

Ай бұрын

Good luck

@floge1

Ай бұрын

good luck friend!

Well made video, here's an algorithm boost!

Very interesting video! I will be taking my first analysis class (convex analysis & optimization) and was a bit worried regarding the notation. Thanks!

@0prcent

Ай бұрын

best of luck!

I would subscribe but you are at 3.14 k subs. Love this video btw; there are not enough videos about symbolic logic on KZread.

Nice Video, I think this explains. I'm a Computer Science Student, I already went through this. Proof by Contradiction is bitch, because it's unintuitive. I hoped you would go s bit more into the detail, because I struggled a lot with this. As far as I understand it know, we want the statement to be true. That's why we can say that if the result is wrong, the condition must also be wrong. It's like a second hidden layer most people say nothing about. Same thing about statements without any quantifier.

@0prcent

Ай бұрын

Thanks for the feedback! And also yeah for implications specifically it might be helpful to review the truth table (which i probably should also have covered in this video now that i think about it) for that operator specifically, then it should make sense why we want both the result and the condition to be wrong.

Wow, thanks zeropercent! This helped me prove Fermat’s Last Theroem! I would include it in this comment, but sadly it’s too long

Very interesting, ty a lot

Really appreciate you using valhalla music

Great video 👍

Cool video, goat montage

Tha Baba is you ost is so good

This would have been very helpful on my first year of uni

Great video! However, a few nitpicks. I think someone mentioned that the "Proof of Contradiction" you talked about is actually Proof by Contrapositive. I do think that the entire section on implications is a bit messy. For example, its confusing to call the contrapositive as the "negation of the implication", as well as the visuals seemingly implying that as well (i.e. both "Condition → ~Result" and "~Result → ~Condition") The connection between if-and-only-if part and implications might be misleading as well. The implications you showed in the video are statements in the object logic, whereas the iff-definitions are in the metalogic. Finally, I do think bringing up negation would be helpful, especially during the latter half. It ubiquitous everywhere, even moreso than "and" and "or".

@0prcent

Ай бұрын

i agree the whole thing about the names of different parts of an implivation even got myself confused while i was making the video, should have made that clearer. i dont think the different usages of if only if would be that confusing to a beginner since it wouldnt really matter to them in the first place and i was thinking about also including negations somewhere but it honestly felt a bit too intuitive for me to specifically talk about them, maybe thats not the case but lets see what other people think as well thanks a lot for taking the time to write down mistakes/things to improve like these, ill take everything into consideration and i really appreciate it!

1:45 "... [an AND expression] evaluates to true..." This is, in my mind, where type theory/constructive logic separates from classical logic: `and` doesn't "evaluate" to anything, but it *is* **proven** when both inputs are proven. (Note, I'm not saying you're wrong -- you're absolutely correct in the classical context --, but I'm highlighting a difference between the classical framework, and a constructive one)

Please continue using cat memes and Minecraft in your editting; it succeeds in making the video (and therefore, its subject) more accessible, and they're adorable!

@0prcent

Ай бұрын

aw thank you! glad that helped with not making it seem too overwhelming

As others pointed out you showcase proof by contrapositive instead of by contradiction If you want to prove A=>B, this statement is equivalent to not B => not A The negation of A=>B is "A and not B", proof by contradiction takes those and leads it to a contradiction such as x=/=x, 1=0,... A lot of proofs for implications by contradiction can be easily turned into proofs by contrapositive since many do not use both A and not B in their deductions, only using not B and the contradiction being "since we assumed A and got not A we have a contradiction" This only really matters for philosophical reasons about validity of the law of the excluded middle and the fact that we are assuming math is consistent, but that is the kind of nitpicky math stuff I personally love

Omg no way baba is you music in a math video lmao. Also, what program did you use for the animations?

@0prcent

Ай бұрын

blender for the 3d animations, manim for the math/latex animations and then edited everything in davinci resolve

Very popular methods lecturers use are proof by it's obvious or proof by it's a task for the student to do in home

If you are a nuroscientist watching tjis or someone you know please aske them this or let us know why we feel sleepy when watching scientific or mathematical explanations content or lectures , is it lack of sleep or how we think during the solution or paying attention or something else completly? im genuinly curious

another way of writing if and only if in a sentence instead of mathematical notation is iff. You can say A is true iff B is true

I have the prooof for the Riemann Hypothesis but there is not enoigh space in the comment to write it.

👌

The subject of a proof is a statement that can be true, or false, or undecidable 😉

how these visualizations are made? btw great video !

@0prcent

Ай бұрын

manim for everything 2d/math stuff, blender for general 3d animations and editing in davinci resolve thanks!

@cutepotato4190

Ай бұрын

@@0prcent impressive work :) waiting for more

@cutepotato4190

Ай бұрын

@@0prcent Thanks man

Does formal proofs using computer theorem provers like LEAN4 ever come up in such courses?

@0prcent

Ай бұрын

i havent really heard of any solvers being covered at uni. not sure what kinda course you would have to attend for that but it would certainly be an interesting topic

@mohamedtalaatharb2441

Ай бұрын

@@0prcent Looks like there are only independent efforts by some professors kzread.info/dash/bejne/eHisktCRdrTSn6g.html and there is also the Xena project. I think it might be useful to include it in education because it looks like there is future potential for it. Imagine being a first year student playing that game adam.math.hhu.de/#/g/leanprover-community/nng4

Baba is you OST at the start of the video.

I think that the Z symbol you used to denote the set of whole numbers is actually used to represent the set of integers. Integers include negative numbers where as whole numbers don't. I don't belive there is a good notation for the set of whole numbers.Generally I'll use N union {0}. Where N is the set of natural numbers.

@0prcent

Ай бұрын

oh just looked it up and i didnt know that "whole numbers" was an ambiguous term. integers is of course what i meant but might be a bit of a translation mistake then, thx for making me aware of this

Your students seems like a pawns, lol. Thanks a lot.

Can you teach us how to proof more advanced topics in mathematics too?

@0prcent

Ай бұрын

There are some things i didnt cover here but as a next step it would probably be best to take a look at some actual proofs (my recommendation would be proof-based book tackling a beginner area of mathematics, i started with analysis back then). I could do another video about advanced proof techniques/tricks but my next video will most likely be about something very different and after getting the basics of proofs down, usually the hardest part is just having an idea

now i am subscribed to lowestpercent *and* zeropercent

As an autodidact, this is a pretty good explanation.

0:58 0:59 1something

This video is proof of the creators genius.

its pretty funny bc in france we do this in 9th grade

Baba is you

now i will be able to prove that i cannot prove this statement!

I don't accept the law of the excluded middle. At least not without some qualifications on what objects are involved.

baba is you

oh wow, set theory.

The title is rather ambitious ?

how to prove anything: 1. make an assertion 2. write "QED" you have now proved (1). QED

Just leave it as an exercise for the reader

proof: I made it up cool vid btw

@0prcent

Ай бұрын

thx!

@cozzy124

Ай бұрын

proof: it was revealed to me in a dream

How to prove anything that can be proven (in mathematics)

8:18 You didn't actually prove the statement is true for all n greater than or equal to 0, since when is between 2 and 4 we get false results. For example 2^2>2^2 is false; 2^3>3^2 is false; 2^4>4^2 is also false.

Did you know that 1+1 = 1. ? In bools algebra that is.

2^3 = 8 < 9 = 3^2

What would be point of math if AI or some else technology will write proofs itself like an oracle or omniscient god? It's kinda math philosophy question because all history humanity lived in some math deficit of proved knowledge even if we had many proved things we always have something to proof

Step 1: Accept reality as real... Or MAYBE Step 1: Assume that you can accept your own assumptions as acceptable. OR maybe Step 1: Accept that concepts exist~~~~~ UUh... Maybe... Step 1: Be alive. Step 2: Watch the video.

my biggest issue with proofs is no one bothers to spell out exactly what they are doing explicitly. too often relying on muh context and muh read my mind. i like programming because you have no choice but to spell out explicitly every minutia of your intended meaning. if only the math world could catch up but it is too bogged down by natural language explanations.

@manawa3832

Ай бұрын

i like what languages like coq and agda are going.

@0prcent

Ай бұрын

i know exactly what you mean, i also come from a programming background and the biggest thing im missing in maths is descriptive variable names. in lots of longer proofs its impossible to track all of the A,B,C,D,x,y,z and 10 different greek letters all being used in conjunction.

🙌 P r o m o s m

How to prove anything: step one: assume 1 = 2

Only because the statement does not work for some negative numbers, it doesn't immediately imply that it is wrong. I don't get why this "proof" should be enough. Btw. n^2>=1 is not true for all negative numbers.

@0prcent

Ай бұрын

remember, n is always an integer

Well if i learned anything it definitely proved that I'm a moron and a dumbass. Since i didn't understand a thing despite watching it 3 times

megga bump

österreicher?

@jorex6816

Ай бұрын

Hab ich auch überlegt

I don’t have to do math

…and YT decided to shadowhammer my comment

@mskiptr

Ай бұрын

(and it seems this one got too) edit: this one only partially

First assertion is wrong. Try again.

❤‍🔥❤‍🔥❤‍🔥