Michael: Or is it 2 million people: *Literaly creaming themselves*

@gracemorales4619

4 жыл бұрын

Fits with your profile picture

@matthewbeggerly52

4 жыл бұрын

OH GOD YES MICHAEL

@dannydazzler1549

4 жыл бұрын

Easily amused

@TheCPtutorales

4 жыл бұрын

That face you make when people overuse the word _"literally"_

@thatcrystalpie

4 жыл бұрын

ew

Alternative title: Michael having fun doing his hobby.

@Novristxch

3 жыл бұрын

Michael is alternate Albert Einstein

@sebmandal

3 жыл бұрын

This stuff is all just so lovely! I’m happy he does this stuff

@iamlordstarbuilder5595

3 жыл бұрын

I had no idea you could prove irrationality. Proofs are a mathematician’s witchcraft.

@dr.theory7900

3 жыл бұрын

He likes it , but I ...

@urlocalcraccdealer954

2 жыл бұрын

or does he?

Proof by contradition is like kryptonite for infinity-related questions, isn't it

@unconscious5630

Жыл бұрын

I mean, proof by induction is more so suited for infinity questions

@joeman1063

Жыл бұрын

@@unconscious5630 what’s proof by induction? I just started discrete math and I don’t think I’ve learned that one yet

@linuslauterbach2975

Жыл бұрын

@@joeman1063 It's basically the domino effect as a method of proof: If you want to show that a statement that somehow depends on a natural number n is true for all natural numbers n, it's sufficient to first show that it is true for n=1 and then show that your statement being true for some n implies it being true for n+1. In other words: you show that the first domino piece falls, and then you show that if some domino falls, the next one will fall as well. Therefore all domino pieces fall and your statement is proven for all n. One typical example for proof by induction is the proof of the closed formula for summing the first n natural numbers provided by little Gauss. Generally a lot of statements involving finite sums lend themselves to proof by induction, for example if you want to show that laws like distributivity hold in general for a finite numbers of addends.

@gauravyadav-bg1bz

Жыл бұрын

Contradiction and Induction method are both same logically. Here your n is a/b , so it holds for any a/b and also a/b + 1 . So by induction this contradiction holds for any a and b ratio.

@gauravyadav-bg1bz

Жыл бұрын

Interesting thing is that,..can we prove existence of God with this method???

I was taught this proof in school yet was somehow still entertained enough to watch the whole video. There is my proof that Michael is an incredible host.

@shamrithponlingam1656

10 ай бұрын

Same

@Gohas09

4 ай бұрын

same

@perseusgaming365

Ай бұрын

same

@RockBrentwood

15 күн бұрын

The proof is like Star-Wars-once-you-see-The-Lord-Of-The-Rings. It's something that looked like "greatness" until you saw what *true* (Academy-Award-Winning) greatness actually looks like, and then you can never go back. Let's do it here now. (1) The Fundamental Theorem Of Arithmetic applies to fractions, too, not just to integers. Every positive rational number has a *unique* factoring into a product of *integer* powers of primes. (2) If q is rational, n is a positive integer, and qⁿ is an integer, then the prime factors of qⁿ all have *non-negative* multiples of n as their exponents. Therefore, the prime factors of q all have non-negative exponents. Therefore q is integer. (3) Therefore, no n-root of any integer z > 0 is rational, unless it's an integer and z = qⁿ is the n-power of an integer. (4) For square roots, that means √z is irrational, unless z = 1, 4, 9, 16, ... for cube roots ∛z is irrational, unless z = 1, 8, 27, 64, ... (or z = -1, -8, -27, -64, ... if you expand this to negative values) and so on.

16:05 the music synchs perfectly with the sound of the pencil drawing on the paper this is extremely satisfying

@Ghost-dh1vv

5 жыл бұрын

This was planned prove me wrong

@Embattled5211

5 жыл бұрын

"synchs"

@hameddesign70

5 жыл бұрын

Damn right X"D

@jannisgehring

5 жыл бұрын

16:06

@Faris-zw7uw

4 жыл бұрын

Omg thats so cute

Rational Ratio I have never realized this and now am freaking out.

@muggtor

4 жыл бұрын

you made me think of other words, and rations, and now im dying

@mariafe7050

4 жыл бұрын

What about irratio?

@mariafe7050

4 жыл бұрын

An irrational number divided by an irrational number. π/e

@unemilifleur

4 жыл бұрын

Never realized that either... I’m French, irrational numbers are called irrationnel, but ratios are called fraction......

@Brunoenribeiro

4 жыл бұрын

you're not alone on this

Literally had this as a proof by contradiction question in a maths test and wanted to curl up in a ball

i really love it when these math videos give me a slight shift in perspective about something that is incredibly common/natural to me-, like, reducing fractions i know in my head that 4/6 is equal to 2/3, easy, and i know that 4/6 can be reduced into 2/3 without changing its value. if you were to ask me _why_ the value doesn't change, my answer would be something like "because the ratio in relation to the numbers stayed consistent, the proportions of 4 to 6 are equal to the proportions of 2 to 3." but here-, michael just gives the simple answer of "since both 4 and 6 can be divided by 2, we can divide this fraction by the fraction 2/2. and since 2/2 is equal to one, this is equivalent to dividing by one, which will not change the value of our number." like-, "huh, that *_is_* true-, it is just like dividing by 1, never thought of it like that" it makes absolute sense and shows a different way to describe the same thing-, it's so cool to me.

@yellingintothewind

8 ай бұрын

Your approach is essentially the geometric proof. Suppose you have two similar right triangles, one with legs of 4 and 6, the other with legs of 2 and 3. For them to be similar, the angles must match, which means the tangent of the angles must match. Since tangent is opposite over adjacent, which is 4/6 for one and 2/3 for the other, those fractions must be the same value.

Michael would be an incredible teacher. Not even just for Maths, he seems to absolutely love learning and teaching

@marialawal7449

2 жыл бұрын

Downside is I dont think teachers get to choose what subject to teach, youtube gives him more freedom and we all get access

@ichthyostegaxd3727

2 жыл бұрын

@@marialawal7449 they do lol why would they teach a subject they're bad at

@dvision4203

2 жыл бұрын

Is he not already a teacher?

@worltex112

2 жыл бұрын

@@ichthyostegaxd3727 They're ✨forced✨, didn't you know?

@ichthyostegaxd3727

2 жыл бұрын

@@worltex112 In which country?

The ancient Pythagoreans would have literally killed you for this act of heresy. They really did not like even the idea of irrational numbers. They drowned the man who suggested that pi might not be some divine ratio like 22/7.

@nabranestwistypuzzler7019

4 жыл бұрын

Robinson Kaspar oh yeah like wtaf was wrong with people in maths and sciences back then?

@garethbaus5471

4 жыл бұрын

@@nabranestwistypuzzler7019 the pythagoreans were more of a cult that thought rational math was the explanation to everything than what would be considered a modern style group dedicated to math or science.

@nabranestwistypuzzler7019

4 жыл бұрын

Gareth Baus Oh wow

@user-vv1do1wg1j

4 жыл бұрын

@@garethbaus5471 a math cult, awesome

@squibble311

4 жыл бұрын

the guy that made this proof was pithagorean. he was killed/banished

Me in Xth class waiting for the statement " To the contrary, lets assume that √2 is rational. "😂😂

@samiatar686

Ай бұрын

and to end with "this contradiction has arisen because of our wrong assumption that √2 is rational " 😂😂

@AbhishekKumar-ql4nq

15 күн бұрын

fr 😂 😂

@madhurmishracss

14 күн бұрын

Indians joined the chat...

@samiatar686

13 күн бұрын

@@madhurmishracss im afghan

This was the first video I've seen on this channel, and I thought that was phenomenal! My favorite math class in college was number theory. I love this kind of stuff. Subscribed.

And today my friends we learned that... Binomial multiplication is Michael's favorite

@tesla_autopilot

5 жыл бұрын

Hs Sm wait until he figures out Pascal’s triangle in polynomial multiplication

@manassable

5 жыл бұрын

(a+b)^2=a^2+2ab+b^2 ... ?

@mikeaft3585

5 жыл бұрын

but he said theyre his fav in a vsauce video

@sardorbekomonkulov6379

5 жыл бұрын

What I see: (a+b)^2 = a^2 + b^2 What others see : (a+b)^2=a^2+2ab+b^2

@sanyalox01

4 жыл бұрын

Sardorbek Omonkulov If you say that (a+b)^2=a^2+b^2, then 2^2 is (1+1)^2, so 2^2 is 2

The way you write "8" gives me nightmares. edit 2 years later: You're free to draw the 8 any way you want, it's on me to not have the nightmares ^^ Also... please buy my indie game? I'm poor. Super Hiking League DX. Thank you.

@mariomario-ih6mn

4 жыл бұрын

Me too

@NesrocksGamingVideos

4 жыл бұрын

@@mariomario-ih6mn Coincidentally, my real name is also Mario. So is my father's.

@mariomario-ih6mn

4 жыл бұрын

@@NesrocksGamingVideos My name is not Mario it's Alexander I named my channel after Super Mario bros

@NesrocksGamingVideos

4 жыл бұрын

Ah cool :)

@remix7345

4 жыл бұрын

its mechanical drawing

As a former Indian 10th class student, I can confirm that our 1st chapter REAL NUMBERS is all about this video. All concepts very well explained.

@wowlittlesam3973

Ай бұрын

yea me too but in our ch it i profed by saying that the result is co prime i was quite intrested to know how actually we condisedered the a=2c part .... never knew it was about even no

@_tarun_

Ай бұрын

true

@user-pz9wh4md4o

Ай бұрын

yeah bro

I know it may seem weird but I have to really thank you bur specifically this video, this honestly helped me getting actually better at math because the first time I watched it it reminded me the deep connection between every mathematical concept and how important are the basics concepts. Today I'm litterally one of the best people in math in my class and I think that this video totally did it part in this, so thank you.

*watches this instead of studying for math test*

@GuitarGuruGaming

5 жыл бұрын

same unfortunately, normal algebra is way more fun than linear algebra

@garrett1644

5 жыл бұрын

Same, pre-calc test tomorrow

@GuitarGuruGaming

5 жыл бұрын

good luck, I bombed mine, hopefully you don't suffer the same fate

@mohammadsharqawi691

5 жыл бұрын

I just watched it after calculas II EXAM, this looks silly but reasonable🤔

@scptime1188

5 жыл бұрын

I think you're mistaken... u don't need to study if you're watching VSauce

How come I’ve never been told “rational” just means “able to be expressed as a ratio”? *I invite you to join the 200+ commenters in advising that I didn't pay attention in school or that ratio is in the word. Please, showcase your originality for us all to see.

@jkgan4952

3 жыл бұрын

Sameee

@danieldavid3766

3 жыл бұрын

You haven't been told that? I pity your school.

@lucasroach7835

3 жыл бұрын

@@danieldavid3766 There's many of us who haven't been told that... esp. if you're not in an english speaking country and rational is a word but ratio isn't

@That_Awesome_Guy1

3 жыл бұрын

@@lucasroach7835 Just add a word meaning ratio to your language. There, problem solved.

@liamreitsma5312

3 жыл бұрын

@@That_Awesome_Guy1 who are you so wise in the ways of science

Okay, this is the best KZread Video I've ever seen. It's so simple, yet so beautiful and inspiring and I think this is, what makes it so good

Thanks for saying zero is an even number. This makes me happy

"Negative... thirteen **exhales in disappointment** is odd"

@koushioni

4 жыл бұрын

-13 = -12 + 1 ¿ *Disappointed*

@augdawg6170

4 жыл бұрын

@@koushioni YOU MEAN NEGATIVE 14!!!

@captcalvin2293

4 жыл бұрын

@@augdawg6170 -13 = 2 x -7 + 1 ¿ *Disappointed* Fixed

@Supertoddy96

4 жыл бұрын

Saw this as it was happening lol

@scritch8833

3 жыл бұрын

@@koushioni that would be -11

When he wrote the decimal number 0.8 and said YIKES i felt that

@lucabrandalesi6743

4 жыл бұрын

My linear algebra professor literally talks about matrices like they are sentients beings. Math teachers are kinda weird

@TheAustronaut03

4 жыл бұрын

yyyyyyOWza

@cosmiro1160

4 жыл бұрын

0:13

@leon_krk

4 жыл бұрын

Then proceeds to dissociate from space time

@TheNuclearBolton

4 жыл бұрын

I wish I was on that kinda high

Some men love money. Some love the smell of napalm in the morning. But the truly scary ones love reduced fractions.

I remember watching this a couple years ago and not understanding a single thing. It feels good watching it today and understanding everything

Everybody gangsta til Michael hits us with that "OR IS IT?"

@nabranestwistypuzzler7019

4 жыл бұрын

Thor Christensen xdxdxd

@yvngdoja

3 жыл бұрын

What im i doin here 😢

@generichomosapien4666

3 жыл бұрын

Yes michael, numbers are lines used by evolved hairy apes to count things, question answered now end the video- “But are we evolved apes? And are numbers really just meaningless lines? First we need to define ape, but what does define mean? First we need to define define so we know how to define apes.”

@shinygreninja4650

3 жыл бұрын

@@generichomosapien4666 but we need to know what is define before defining define. So we end up in a loop. I dont know how to end this, I'm confused, choose one of the two below 1. But what is a loop? *VSauce music plays* 2. OR DO WE?

@unkn0vvnmystery

3 жыл бұрын

or are they?

That's why I love maths. I think it's really interesting how you play with numbers to solve/prove things.

This is literally 8th-9th grade exact maths, he is teaching in such a way that its part of our dopamine dose. Amazing

having ptsd flashbacks of doing proofs for exams

@cjaune909

5 жыл бұрын

Haii

@ZoraLink4

5 жыл бұрын

Music man make more music.

@majortom4543

5 жыл бұрын

No, i was watching like 6 minutes of the video and then realized i was thinking about other things while listening michael speaking something faint in the background. But i was still watching the video. It feels amazing but its so sad that i zone off and moom fail

@drsuqi

5 жыл бұрын

I'm currently doing that

@TheGerm24

5 жыл бұрын

Yep, I felt like I was back in college math classes. I remember doing the even/odd proofs.

Irrational? Like Michael’s decision to not upload on the main channel ever?

@NicoFye

5 жыл бұрын

Ahaha

@danebradbury5940

5 жыл бұрын

He spends months on making the main channels vids so they are as detailed as possible but on dong he can make quick vids also he definetly makes less money making those than other things he could be doing.

@danebradbury5940

5 жыл бұрын

He has said why before

@kartonbaba

5 жыл бұрын

even if he uploaded a video of a compilation of his "hi vsauce, michael here", i would watch it

@jacquesburger4103

5 жыл бұрын

This is too damn true... The extro said Vsause tho so idk

Great video! This gave me flashbacks to when i was first learning how to do a basic proof. I just know younger me would have just kept going back and forth proving the various variables were even and completely missing what i was even supposed to be doing.

Memories; Your video was fun to visit. It brought back my intro to my mathematics studies. Your presentation was well done. Thank You.

Let's prove that the square root of 2 is irrational... BUT FIRST! What is a number?

@augusttyellis

4 жыл бұрын

...and how much does a number weigh?

@BerlinWallNeverFall

4 жыл бұрын

And where is it in time

@edwardwong9599

4 жыл бұрын

Can I eat it?

@emmatcr5783

4 жыл бұрын

It's odd to have even numbers..

@Burdarper

4 жыл бұрын

... and how does it smell in space ?

*Y O W Z A S*

@yohansaldana8218

5 жыл бұрын

What's that?

@yohansaldana8218

5 жыл бұрын

@@NodenGaming ???

@johnnyjoestar6478

5 жыл бұрын

christian Saldaña 11:22

@yohansaldana8218

5 жыл бұрын

Oooooohhhhhh...okay.

@egorovcharenko7014

4 жыл бұрын

Яуза ))) A river in Moscow!

I can't believe I watched the whole video. This was surprisingly very entertaining. I wish my math teachers had been like him

And this proof works for the square root of any non perfect square numbers

2:32 when u are not sure of ur answer on a math test

@daslynnter9841

5 жыл бұрын

14:25 when you are not sure of an answer in an open book math quiz

@sethdavis6198

5 жыл бұрын

So good😂

@undyneultra8958

5 жыл бұрын

i had a math test in my school today

@emmanuelpil

5 жыл бұрын

If √2 can't be the exponential of 2 can't be either.

@koulatko1171

5 жыл бұрын

Exactly. I also love how the thing continues all the way to 2:51

I wish someone would look at me the way Michael looks at the number 8.

@ProudlyIdiotic

2 жыл бұрын

Oooh look at the beauty

@dvision4203

2 жыл бұрын

You’ll find them ☺️

@user-fw1bu6fd2i

2 жыл бұрын

Sorry, I cannot keep looking at you. You are just too bright 😎

@flamingaish

2 жыл бұрын

Lmfao

Damn these videos are so compelling to watch. Michael's enthusiasm and simple explanations are captivating.

I loved your video. I hadn’t felt so much emotion since abstract algebra. Keep up the great work, man.🎉🎉

The way he subtly integrates easy to understand definitions for complex and simple math at the same time is incredible and would make it very easy for children to learn if teachers did math like this.

@scellyyt

Жыл бұрын

sad life

@skrimish7145

Жыл бұрын

the difference is teachers teach multiple children all at once. Here michael is almost talking to you one on one and i dont think teachers get paied enough to have a full conversation w/ all their kids about the subject.

@Azmyuth

Жыл бұрын

@@skrimish7145 except he's not asking you questions or anything that is impossible to do with multiple people, the teacher could write all this on a board (or paint if they're online), and then ask questions after to verify.

@henry497

8 ай бұрын

@@skrimish7145 a youtube video is quite literally the polar opposite of a one on one conversation. This video could be a conversation with everyone in the world at the same time.

@Lemony123

7 ай бұрын

@@henry497 I mean, A teacher cannot check all student at the same time.

Did anybody notice at 00:13 he distorted himself when he said yikes lol

@theogarcez1999

3 жыл бұрын

LOL

@Marispider

3 жыл бұрын

*"y i ḱ e̳͠ s҉ s̤̩̜̬̝͍͞ s̴̨̢̠̳̹̖͎̺ s҉̶̹̜̟̖̬̘̬̦͓̪̺̙ͅ ş̸̴҉̭͓̰̫͎͚ s̵̞̬̳͍̥͙̪͔̎͒̓ͧ͠ͅ s̢̞̥͓̗̩̠̙̩͇̥̰͕̬̟̃̐ͪ͛͗̚͠"*

@javeinne

3 жыл бұрын

yup

@andyb3773

3 жыл бұрын

I did not lmao

@burcburc865

3 жыл бұрын

I though it's just my eyes so I didn't replay that part until now. lmao

You learn this in undergraduate linear algebra. It was very useful for me to have seen this video years before we covered this topic, as it really made it easy to get into.

This is for me the best video to introduce maths to literally everyone.

'Unless our teachers have been lying to us our entire lives' "YoU wOn'T aLwAyS hAvE A cAlCuLaToR wItH yOu"

@mohiburrahman8331

3 жыл бұрын

Here most of the job related exams don't allow calculator imoooo 😭😭😭😭

@dewut420

3 жыл бұрын

@@mohiburrahman8331 Practice maketh perfect

@mailbox3982

3 жыл бұрын

Oh yeah one of my teachers told me that so i carried a calculator in my pocket for five solid months straight. The teacher was not amused.

@martingouws3876

3 жыл бұрын

You carry a library containing more books than the one in Alexandria, and a calculator and a supercomputer in your pocket. Try going back in time to tell your teachers that😅 Oh wait, we don't carry a time machine in our pockets, YET

@Owen_loves_Butters

2 жыл бұрын

Well to be fair they didn’t lie, they just didn’t know

I have seen this proof maybe 50 times now, but no one gets as hyped as Michael. I love it! "OH MY GOODNESS GRACIOUS! IT'S EVEN!!!!"

Why does vsauce write his 8 like that?

@bulamulafula3555

19 күн бұрын

Don’t question the sauce.

@shikharmishra3595

Күн бұрын

i am pretty sure he calls us vsauce and himself micheal, you know, like in every video he says "hey vsauce, micheal here"

The way he writes “8” hurts my eyes.

@lordwarlockthangwrath8662

12 күн бұрын

How come?

Me: Doesn’t like math Also me: watches man do math for 17 minutes

@haydenboyer9193

4 жыл бұрын

Can relate

@OGrupxe

4 жыл бұрын

I mean, Michael somehow teaches way better than my math teacher. Don't know about you guys.

@keemo4647

4 жыл бұрын

@@williammay451 same

@marcel7922

4 жыл бұрын

It's not that you don't like math, it's that you have been taught to fear math by the school system and bad teachers. Math by itself can be fun when it's not connected to pressure.

@fliiiou6388

4 жыл бұрын

I'm your 666th like, you're now the devil

He draws "8" like I'm back in primary school

@hardscope8529

4 жыл бұрын

Yaaa thought the same.. xD

@st4ndby

4 жыл бұрын

That irritated me so much 😄

@steelforge8577

4 жыл бұрын

@@williammay451 Or did you?

@keemo4647

4 жыл бұрын

@@steelforge8577 I mean what is writing (vsause music starts)

Now if only my math instructors in school could have explained things as thoroughly and with such enthusiasm, instead of just glossing over everything.

This video is so comprehensible and deeply inspiring, thank you for such a wonderful video.

15:40 "Oh my goodness gracious!" Lol. Getting so excited for an even number

@aleksandarvlasev4030

5 жыл бұрын

It's like he can't even

@bethmil705

5 жыл бұрын

@@aleksandarvlasev4030 LOL

@mustafarahi8670

5 жыл бұрын

+Alexander Vlasev u made my day 😂

2:31 he says the thing

@Noah-gn5re

5 жыл бұрын

What even is that pfp

@rexevan6714

5 жыл бұрын

ROLL THE 🎶

@Fassle

5 жыл бұрын

it scares me

@fastandbulbous9697

5 жыл бұрын

I unironically want to kiss Cirno's ocks on your profile picture

@joshuaosei5628

5 жыл бұрын

Or did he?

always fun to rewatch these videos years later now i know more about mathematics and statistics and so on

One minor issue. The statement "a^2 is even implies a is even" doesn't follow from "a even implies a^2 even". It follows from the contrapositive of the statement "a odd implies a^2 odd". In this case it seems trivial but the phrasing comes off as "A implies B is true because B implies A is true", which in general is NOT logically true. Converses are not equivalent statements, but contrapositives are.

@Lucashallal

Жыл бұрын

Excellent point

He protecc He attacc But most importantly, He bacc

@hussaina.4431

5 жыл бұрын

... on the wrong channel

@jtjs2890

5 жыл бұрын

Second comment

@frogenthusiast4017

5 жыл бұрын

@@jtjs2890 why u gotta announce that

@sorako04

5 жыл бұрын

VN :)))

@hoangao437

5 жыл бұрын

Though Kevin and Jake are still active

God if every math teacher was like this everyone would have their Master's

@mikkihintikka7273

3 жыл бұрын

yeah like in 40 years

@Jack-do5tq

3 жыл бұрын

@@mikkihintikka7273 lol

@padmanabanraghavendran3570

3 жыл бұрын

Yep , the video was just him explaining basic algebra most of the asians already learnt in 6th or 7th grade Idk about western education tho

@mikkihintikka7273

3 жыл бұрын

@@padmanabanraghavendran3570 yep and they learn it in tenth of the time

@youreyesarebleeding1368

3 жыл бұрын

@@padmanabanraghavendran3570 western education is optional beyond algebra and some geometry. Highschool usually has you take algebra 1 and 2, geometry, and trigonometry or pre calculus. After that, in college, a lot of degrees only require like... Calc 1 which is pretty easy, you learn derivatives, optimization, integrating, implicit derivatives, and stuff like that mostly. In some majors you have to take more, like I am a CS major and i have to take calc I, II, III, and then either calc IV or Matrix Algebra. If i take two extra math courses which i can easily do over summer or something, I will actually be able to get my minor in math. All engineering majors are about the same in that regard

There's an oversight in this proof. The fact that an even number squared is also even does not mean that the root of an even number is necessarily squared. This needs further proof, if we are to remain rigorous.

@Adventurer-te8fl

6 ай бұрын

Yes, however, in this proof, a and b are defined to be integers in the initial assumption

You explained this better in 17 minutes than my math teacher in 45 minutes did

Did I ask for this? Absolutely not Did I need this? Absolutely not Did I love this? Absolutely

@Tiernan422

3 жыл бұрын

Not

@rhymescheme1194

3 жыл бұрын

Did i need to tell this: Absolutely not Am i telling this: Absolutely I am your 111th like

@riooo8072

3 жыл бұрын

i needed this

@shinygreninja4650

3 жыл бұрын

@Modar Bilal01 but first let us see, what is need...

@realeyes8199

3 жыл бұрын

I needed this

Maybe it's irrational because of a traumatic experience

@-_Nuke_-

5 жыл бұрын

@@owltaku5757 xD

@barrackoli

5 жыл бұрын

It saw 7 8 9

@bard119

5 жыл бұрын

What if the number 2 identifies as a 3?

Learning more info from KZread in 17 minutes than my school can provide in an entire lesson, math edition

This is the video I would like to make myself. But, it could never be as good as this, so now I’m not going to bother!

Binomial Multiplication: *appears* Me: So we meet again...

@squibble311

4 жыл бұрын

how did u americans not learn that (x+y)² = x²+2xy+y²

@pearlphosphophyllite995

4 жыл бұрын

@@squibble311 No, I am not American, and yes, I did learn that.

@sanyalox01

4 жыл бұрын

Meanwhile i know that (x+y)^5=x^5+(x^4)(5y)+10(x^3)(y^2)+10(x^2)(y^3)+(5x)(y^4)+y^5

@jacksonbrewer2380

3 жыл бұрын

sini harshan we did learn it. It’s not hard

@padmanabanraghavendran3570

3 жыл бұрын

@@jacksonbrewer2380 idk about western education (i heard it is slow) but asians learn basic algebra at 5th or 6th grade

Hey Vsauce, Michael here. Vsauce is my main channel Or is it? 🎵🎵🎵🎵🎵

@RAHISTILLL

5 жыл бұрын

Hahaha I love this comment

I find it really beautiful that the sqrt(2) is the ratio of 2 even numbers. Numbers so even that their ratio is irrational. Its really fitting for 2, the most quintessentially even number, that at its root is numbers so even our minds cannot comprehend it, in a way.

@DOROnoDORO

Ай бұрын

sqrt(2) cannot be expressed as the ratio of two even numbers

This is pretty cool. I'm currently in an introductory abstract math course and I'm learning almost exactly these things.

Wait, Michael writes 8 as one circle on top of another.

@lordelmo6959

5 жыл бұрын

Let him live in peace with his circle 8.

@BertGrink

5 жыл бұрын

this reminds me of a joke i once read: two zeroes are trekking though the desert when they spot an eight under a palm; one zero says to the other: i can't understand how they can do it in this terrible heat.

@KenmoreChalfant

5 жыл бұрын

THERE ARE DOZENS OF US

@utube4204

5 жыл бұрын

Normies

@eshan309

5 жыл бұрын

Y O O O O W Z E R S

Can we rename this channel to Vsauce4 - Mainly DONG and sometimes Original Vsauce

@dumbasgenius7227

5 жыл бұрын

I love this kind of stuff and its actually the main reason i am subbed. I miss the original Vsauce videos and he hasn't uploaded anything but mindfeild for so long. This kindof stuff should go of Vsauce 1

@cosmiccreeper247

5 жыл бұрын

Or just new vsauce 1 then rename vsauce 1 to vsauce premium

@fhz3062

5 жыл бұрын

This is Vsauce4 - Ponto em Comum (Made in Brazil): kzread.info/dash/bejne/Yq5mutydoaSzhrQ.html It is an amazing documentary about vaccines. "Olá Criaturas da Internet, aqui quem fala é Davi Calazans." SAP: Hey Vsauce, Davi Calazans here.

Probably one of the best math teacher I have ever seen. And arguably the best on KZread.Just Superb

Never seen someone so excited about the definition of even and odd 😂

This is kind of a fusion of numberfile and vsauce And for some reason it is on DONG

i wish my math teachers were as engaging as you, god damn

@Tor.G

5 жыл бұрын

Math teachers are.. but they have to teach you both how to do, and why to do.... and a lot more than just one thing. Most of class would not be able to follow this anyway.

@HeroRaze

5 жыл бұрын

it's hard to get your students' eyes to zoom in on your face at comedic moments

@shinydewott

5 жыл бұрын

Ryan G-P underrated comment

@jamesramirez0408

5 жыл бұрын

0:12

@DavidDias7

5 жыл бұрын

@@Tor.G why wouldn't they. While I agree there's a plan the theachers have to follow this is basic math, most youngsters out there would understand pretty quickly

I just finished my chapter real numbers and learn about proving Irrational and KZread recommendations this to me

My favorite moment is when Michael finishes the proof. We all knew where this was going. Michael certainly knew where this was going. But that moment facial catharsis after drawing those final two underlines at 16:39 is the pure feeling of discover, understanding, and enlightenment.

@stratonikisporcia8630

Жыл бұрын

I mean Aristotle knew where this was going, and for reminder he didn't even know that the Earth was spinning around the Sun

Michael: writes 8 as two circles instead of a single interlocked line Everyone, while going through content aware scale: *ＹＩＫＥＳ*

@user-fs3ch6cc3j

2 жыл бұрын

8 as two circles are quite.. perfect to look at. You can replay the beginning to see that. Granted.. it can take a bit longer to move your wrist and draw the other circle than to do it in a continuous line :P

@Hugowtum

2 жыл бұрын

@@user-fs3ch6cc3j yeah, everytime i write an 8 there will always be a point coming out of it, that trigger me everytime, and i do it with a single line.

@noobeleman13ylonce69

2 жыл бұрын

yikes

@scibanana3542

Жыл бұрын

I write my 8's as 2 circles. Just because it's not the most common way of doing so doesn't mean there's anything inherently wrong with it.

@traywor1615

Жыл бұрын

What does it mean to be going through content aware scale?

When you wake up on Monday and remember that you didn't do ur homework 0:13

@jordymottershead

4 жыл бұрын

haha

@Schmlif6090

4 жыл бұрын

underrated

@DanS044

4 жыл бұрын

I didn’t notice how he wiggled XD

@carsonmorris127

4 жыл бұрын

Dan Slater woah I just noticed that

@rahimeozsoy4244

3 жыл бұрын

Oww....

Beautiful! Understood more than ever in classes, in school!

This has and will forever be my favorite proof. Simple, elegant, and easy.

Michael: * says something * me : yes yes very good * stares intensely at t-shirt *

@saral9817

5 жыл бұрын

Hello reyan

@user-or9hk4uz7g

5 жыл бұрын

close but no cigar ;-; anyway hi ¯\_(ツ)_/¯

Me: I already know this proof, it’s pretty basic, I’ll just move on ... *clicks anyway*

@xxcsokixx

3 жыл бұрын

Yup. I had to learn it when graduated from high school 3 years ago. Still nice to refresh your brain with some lovely smiling 'or is it' Michael.

@realbignoob1886

3 жыл бұрын

I had to learn it in middle school...

@stephendonovan9084

3 жыл бұрын

@@can.of.beans101 It seems I did, good thing you remembered to write one for me. Thanks champ :)

@petrapinter349

3 жыл бұрын

@@stephendonovan9084 that comeback😳

@DrexYiii

3 жыл бұрын

OR IS IT BASIC?

I used to think the square root of 2 was just another number, but it turns out it's the sneakiest number of them all!

man i needed that proof for my sophomore exams but did not expect vsauce to have a video on it

Sorry if I'm dumb but I don't really get it. For me the proof Michael shows at 5:55 only proves that an even number squared always produces an even number, NOT that the square root of any even number is also an even number. For example the square root of 6 isn't an even number, since by definition an even number has to be an integer (not a fraction). And this kinda ruins the whole proof at the end in my mind. Pls help me out. Edit: Ok I finally get it, for those that are still confused I hope this clears it out (thanks to FlamingJM for making me understand it fully): The proofs at 5:55 indeed don't prove that the square root of any even number is also an even number, like I said. They just prove that all even integers squared produce even numbers, and all odd integers squared produce odd numbers. This means that IF the square root of an even number is an integer, then it must itself also be an even integer, (it can't be an odd integer since all odd integers squared produce odd numbers). In the final proof at the end, we know that a and b are integers (because numerators and denominators in a fraction are always integers after all). Therefore since by squaring either of them you get an even number, they themselves must also be even numbers. All of this means that if the square root of an even number is not an integer, then it must be an irrational number. Apparently this applies to odd numbers too. So the square roots of not just 2, but all other non-square numbers, are also irrational numbers. I only learned this now. Hope this helps. And as always, thanks for watching!

@TheUltimateDavyGravy

5 жыл бұрын

the square root of 6 is also an irrational number, just like the square root of two, so you've basically just discovered the same contradiction that Michael uses to prove that the square root of two is irrational

@Capstfu

5 жыл бұрын

I thought we all knew that most even numbers have irrational square roots 🤷🏾‍♂️

@FlamingJ999

5 жыл бұрын

Remember that he defined a and b to be integers. This means that a² and b² are squares of integers. While it is true that sqrt(a) is not necessarily an even integer if a is an even integer, we know that a is an integer, and we're squaring it to get a². So if a² is an even integer, we know that a (the integer that was squared to get a²) is also an even integer.

@jasonroyer9870

5 жыл бұрын

He doesn't prove that the square root of an even number is even, but rather the square root of c^2 (where c represents an even number) is even, which is common sense: squaring and square root-ing cancel reach other out and oh my God you have over a million subs

@FlamingJ999

5 жыл бұрын

Another way to think about it is that, since he proved that all odd numbers squared are odd, and a² is even, then a is definitely not odd (he already defined a to be an integer) thus a is even.

14:07 "Oh my goodness gracious" 15:40 "Oh my goodness gracious"

@ElCholoDeJolo

5 жыл бұрын

Look at that. LOOK AT THAT

@rachaeljameson2641

5 жыл бұрын

look at what we have now!

@antonknittel3541

5 жыл бұрын

Thanks

Its been more than 10 years since I left my school, and this video made me understand why multiply becomes divide on the other side of the equation and vice versa. I was never told why just taught what.

I love how the comments here are so calm and reasonable, meanwhile in vsauce it's pure chaos

Micheal: Do you know what an even and an odd number are? Me: I do! Micheal: ...or do you? Me: 😦😦😦

@sickomode2761

4 жыл бұрын

Alex Baldwin how did you spell it wrong twice

@bugjams

4 жыл бұрын

@@sickomode2761 Micheal? That's how autocorrect tells me to spell it. :(

@mariafe7050

4 жыл бұрын

Alex Baldwin Can you turn off autocorrect?

@platypuschallenger

4 жыл бұрын

Spelled 'Michael'

@sharkronical

4 жыл бұрын

It's Mikál

I too enjoy binomial multiplication.

@DerpMuse

5 жыл бұрын

as if theres any other kind

@MinecrafMobber

5 жыл бұрын

it's all about polynomial multiplication

@joaopedrobahienseegashira1069

5 жыл бұрын

Think about remarkable products...

@Alkaloid-Odin

5 жыл бұрын

Ah a fellow intellectual, I see.

@lily-vt8ic

5 жыл бұрын

I do not. Especially when it involves exponets and 2 variables.

That was actually pretty beautiful

I can sense this man is put out of context very often

Michael looking at 8 : *ahegao faces* Michael looking at 0.8: *incoherent screaming*

the way Michael writes the number 8 is mildly infuriating

@SuperTurtle0

5 жыл бұрын

Ethanagor S-D that’s how I write 8s

@alexandergeppert3174

5 жыл бұрын

@@SuperTurtle0 youre a bad person

@SuperTurtle0

5 жыл бұрын

Alexander Geppert not my fault I’ve always written them that way

@TotalImmort7l

5 жыл бұрын

@@SuperTurtle0 style, eh?

@mrgraystripe1373

5 жыл бұрын

But it looks much better

Bro proved 0 even in 4 minutes

I'm on a physics degree but somehow Vsauce michael is the first person to tell me the rational ratio name thing.

Dong status: fully expanded.

@the711devin4

5 жыл бұрын

Channel name “Dong”: fully retracted.

@remlo5482

5 жыл бұрын

D!NG*

@add852

5 жыл бұрын

Mandela Effect at it's finest

@FrozakRL

4 жыл бұрын

Add 852 ??

@MrMan-np9jg

4 жыл бұрын

@@remlo5482 r/woosh

i was lost from the moment he said : "hey vsause micheal here" wait..... he didnt say it in almost a damn year now !

Vsauce saying "yikes" with the distortion filter just made me giggle

At about 16:00 he says "since an even number squared is even, then if b^2 is even then b must be even". That is using the implication in the wrong way.

@kyuta001

8 ай бұрын

fr

@Adventurer-te8fl

6 ай бұрын

The reason why it’s ok is because in the assumption, he said that a and b are integers. But yes, if we didn’t know that b was an integer, it would be using the implication in the wrong way.

Let’s just take a moment to appreciate how straight all of his lines are.

@oldmanjeffrey

2 жыл бұрын

Those things were straighter than I am! But that’s not saying much.

@theAWPspammer

2 жыл бұрын

@@oldmanjeffrey ayo

@ablemoo

2 жыл бұрын

@@oldmanjeffrey 😏😏 okay daddy