16:05 the music synchs perfectly with the sound of the pencil drawing on the paper this is extremely satisfying
@Ghost-dh1vv5 жыл бұрын
This was planned prove me wrong
@Embattled52115 жыл бұрын
"synchs"
@hameddesign705 жыл бұрын
Damn right X"D
@jannisgehring5 жыл бұрын
16:06
@Faris-zw7uw5 жыл бұрын
Omg thats so cute
@Rio-cs6nx3 жыл бұрын
Alternative title: Michael having fun doing his hobby.
@Novristxch3 жыл бұрын
Michael is alternate Albert Einstein
@sebmandal3 жыл бұрын
This stuff is all just so lovely! I’m happy he does this stuff
@iamlordstarbuilder55953 жыл бұрын
I had no idea you could prove irrationality. Proofs are a mathematician’s witchcraft.
@dr.theory79003 жыл бұрын
He likes it , but I ...
@urlocalcraccdealer9542 жыл бұрын
or does he?
@Brunoenribeiro Жыл бұрын
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???
@ryane5281 Жыл бұрын
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 Жыл бұрын
Same
@Gohas098 ай бұрын
same
@perseusgaming3655 ай бұрын
same
@theNotoriousBFM2 ай бұрын
this was my first hw assignment in math class in college. solving it made me taste the tip of the iceberg of math. a start of a life long love affair with the subject.
@thingthingthingthingthingthing20 күн бұрын
666 likes hahahaha
@DrizzletGaming5 жыл бұрын
Michael: Or is it 2 million people: *Literaly creaming themselves*
@gracemorales46195 жыл бұрын
Fits with your profile picture
@matthewbeggerly525 жыл бұрын
OH GOD YES MICHAEL
@dannydazzler15495 жыл бұрын
Easily amused
@TheCPtutorales5 жыл бұрын
That face you make when people overuse the word _"literally"_
@thatcrystalpie5 жыл бұрын
ew
@robinsonkaspar33954 жыл бұрын
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.
@nabranestwistypuzzler70194 жыл бұрын
Robinson Kaspar oh yeah like wtaf was wrong with people in maths and sciences back then?
@garethbaus54714 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.
@nabranestwistypuzzler70194 жыл бұрын
Gareth Baus Oh wow
@user-vv1do1wg1j4 жыл бұрын
@@garethbaus5471 a math cult, awesome
@squibble3114 жыл бұрын
the guy that made this proof was pithagorean. he was killed/banished
@dylanwakefield7466 Жыл бұрын
Literally had this as a proof by contradiction question in a maths test and wanted to curl up in a ball
@Alchemistic883 ай бұрын
Michael... Can you please pay Terrence Howard a visit.
@mattschemmer3091Ай бұрын
Terrence is where he is because he refuses to listen to people. He doesn't care. He's your typical slightly-smarter-than-average person who wishes he was the smartest person in the world, but the only way for that to be true is for everyone smarter than him to be wrong. His goal isn't to find useful truths.
@kekero5404 жыл бұрын
Rational Ratio I have never realized this and now am freaking out.
@muggtor4 жыл бұрын
you made me think of other words, and rations, and now im dying
@mariafe70504 жыл бұрын
What about irratio?
@mariafe70504 жыл бұрын
An irrational number divided by an irrational number. π/e
@unemilifleur4 жыл бұрын
Never realized that either... I’m French, irrational numbers are called irrationnel, but ratios are called fraction......
@Brunoenribeiro4 жыл бұрын
you're not alone on this
@invaderaid72163 жыл бұрын
Michael would be an incredible teacher. Not even just for Maths, he seems to absolutely love learning and teaching
@marialawal74493 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
@ichthyostegaxd37272 жыл бұрын
@@marialawal7449 they do lol why would they teach a subject they're bad at
@dvision42032 жыл бұрын
Is he not already a teacher?
@julianw10102 жыл бұрын
@@ichthyostegaxd3727 They're ✨forced✨, didn't you know?
@ichthyostegaxd37272 жыл бұрын
@@julianw1010 In which country?
@NaraASMR Жыл бұрын
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 Жыл 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.
@nexor78093 ай бұрын
so why would i ever need that and why was it taught in schools again?
@manghariz2211Ай бұрын
@@nexor7809 Seriously? This is so elementary that this is going to be used in your everyday life, the use of the concept of fraction is so ubiquitous to explain quantities in comparison to other quantities as example. If you don't understand that fractions can be reduced, you are going to be easily fooled by people intentionally misleading you.
@nexor7809Ай бұрын
@@manghariz2211 no
@jackpot60563 ай бұрын
Who else is here after watching the Terrence Howard video?
@OneWhoKN0ZE2 ай бұрын
We are being watched and listened to. 😂
@bakedpotato4202 ай бұрын
Me 😂
@GeerHedVR2 ай бұрын
Me 😂
@Alexlabtester2 ай бұрын
Pretty much
@Friend.from.school2 ай бұрын
Hahahaha that’s what made me watch this
@natesullivan60864 жыл бұрын
Doctor: What would you like to name your child? Michael: I think i'll call it "c".
@bukucinho4 жыл бұрын
Nate Sullivan I c what you did there
@filip95644 жыл бұрын
@@bukucinho i wanna B as cool as you
@anomonususer86264 жыл бұрын
Filip but U and I can’t
@anomonususer86264 жыл бұрын
Tor McLean at least you R continuing it like us
@anomonususer86264 жыл бұрын
ichbin luis Y
@mahejabeenfatima21288 ай бұрын
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.
@wowlittlesam39735 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_5 ай бұрын
true
@user-pz9wh4md4o4 ай бұрын
yeah bro
@BrocNerd3 ай бұрын
someone send this video to terrence howard and joe rogan
@nancyzipperer8819Ай бұрын
I'm pretty sure that's what Terrance was trying to say
@ferretyluv22 күн бұрын
@@nancyzipperer8819No he wasn’t. He thinks sqrt2 is exactly 1.
@Cyranek5 жыл бұрын
having ptsd flashbacks of doing proofs for exams
@cjaune9095 жыл бұрын
Haii
@ZoraLink45 жыл бұрын
Music man make more music.
@majortom45435 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
@drsuqi5 жыл бұрын
I'm currently doing that
@TheGerm245 жыл бұрын
Yep, I felt like I was back in college math classes. I remember doing the even/odd proofs.
@NesrocksGamingVideos4 жыл бұрын
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-ih6mn4 жыл бұрын
Me too
@NesrocksGamingVideos4 жыл бұрын
@@mariomario-ih6mn Coincidentally, my real name is also Mario. So is my father's.
@mariomario-ih6mn4 жыл бұрын
@@NesrocksGamingVideos My name is not Mario it's Alexander I named my channel after Super Mario bros
@NesrocksGamingVideos4 жыл бұрын
Ah cool :)
@remix73454 жыл бұрын
its mechanical drawing
@mariomio86513 ай бұрын
Someone should send this video over to Terrance Howard I think he needs it.
@hindsight20223 ай бұрын
Terrance howard enters the chat:
@bakedpotato4202 ай бұрын
It's hard out here for a pimp, Mayne.
@vikings-pistons2 ай бұрын
Terrance howard is too dumb and/or delusional to comprehend this video
@paularobinson82862 ай бұрын
@@bakedpotato420❤
@keelanbrown77474 жыл бұрын
Did anybody notice at 00:13 he distorted himself when he said yikes lol
Me in Xth class waiting for the statement " To the contrary, lets assume that √2 is rational. "😂😂
@samiatar6865 ай бұрын
and to end with "this contradiction has arisen because of our wrong assumption that √2 is rational " 😂😂
@AbhishekKumar-ql4nq4 ай бұрын
fr 😂 😂
@madhurmishracss4 ай бұрын
Indians joined the chat...
@samiatar6864 ай бұрын
@@madhurmishracss im afghan
@apolloismydad2 ай бұрын
bro how was ur exam?
@michaelhudson41925 жыл бұрын
*watches this instead of studying for math test*
@GuitarGuruGaming5 жыл бұрын
same unfortunately, normal algebra is way more fun than linear algebra
@garrett16445 жыл бұрын
Same, pre-calc test tomorrow
@GuitarGuruGaming5 жыл бұрын
good luck, I bombed mine, hopefully you don't suffer the same fate
@mohammadsharqawi6915 жыл бұрын
I just watched it after calculas II EXAM, this looks silly but reasonable🤔
@scptime11885 жыл бұрын
I think you're mistaken... u don't need to study if you're watching VSauce
@ThorHC114 жыл бұрын
Everybody gangsta til Michael hits us with that "OR IS IT?"
@nabranestwistypuzzler70194 жыл бұрын
Thor Christensen xdxdxd
@yvngdoja4 жыл бұрын
What im i doin here 😢
@generichomosapien46664 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.”
@shinygreninja46503 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?
@unkn0vvnmystery3 жыл бұрын
or are they?
@UteChewb2 ай бұрын
This is a beautiful introduction about how mathematics is done. Exploring to find the proof.
@d3vilman693 ай бұрын
When I come across the term "rational numbers", I never imagined "ratio" comes to mind. I simply thought they are numbers that "makes sense". Very educational video indeed. Especially the concept of proofing via contradiction. Please make a video to proof that 1+1=2
@just-a-silly-goofy-guy5 жыл бұрын
Irrational? Like Michael’s decision to not upload on the main channel ever?
@NicoFye5 жыл бұрын
Ahaha
@danebradbury59405 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.
@danebradbury59405 жыл бұрын
He has said why before
@kartonbaba5 жыл бұрын
even if he uploaded a video of a compilation of his "hi vsauce, michael here", i would watch it
@jacquesburger41035 жыл бұрын
This is too damn true... The extro said Vsause tho so idk
@ThePlatypusAvenger5 жыл бұрын
When he wrote the decimal number 0.8 and said YIKES i felt that
@lucabrandalesi67434 жыл бұрын
My linear algebra professor literally talks about matrices like they are sentients beings. Math teachers are kinda weird
@TheAustronaut034 жыл бұрын
yyyyyyOWza
@cosmiro11604 жыл бұрын
0:13
@leon_krk4 жыл бұрын
Then proceeds to dissociate from space time
@TheNuclearBolton4 жыл бұрын
I wish I was on that kinda high
@keyanchaudhri85698 ай бұрын
Why does vsauce write his 8 like that?
@bulamulafula35554 ай бұрын
Don’t question the sauce.
@shikharmishra35953 ай бұрын
i am pretty sure he calls us vsauce and himself micheal, you know, like in every video he says "hey vsauce, micheal here"
@elisabellesi Жыл бұрын
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.
@Deltexterity5 жыл бұрын
2:32 when u are not sure of ur answer on a math test
@daslynnter98415 жыл бұрын
14:25 when you are not sure of an answer in an open book math quiz
@sethdavis61985 жыл бұрын
So good😂
@undyneultra89585 жыл бұрын
i had a math test in my school today
@emmanuelpil5 жыл бұрын
If √2 can't be the exponential of 2 can't be either.
@koulatko11715 жыл бұрын
Exactly. I also love how the thing continues all the way to 2:51
@MegaSuperCritic3 жыл бұрын
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.
@jkgan49523 жыл бұрын
Sameee
@danieldavid37663 жыл бұрын
You haven't been told that? I pity your school.
@lucasroach78353 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_Guy13 жыл бұрын
@@lucasroach7835 Just add a word meaning ratio to your language. There, problem solved.
@liamreitsma53123 жыл бұрын
@@That_Awesome_Guy1 who are you so wise in the ways of science
@Tomkat53 Жыл бұрын
Damn these videos are so compelling to watch. Michael's enthusiasm and simple explanations are captivating.
@andrewbirch64863 ай бұрын
Absolute breath of fresh air after listening to 3hours of Terrence Howard rambling on jre
@DaumbFauckProduction3 ай бұрын
explain?
@matthewhue3 ай бұрын
@@DaumbFauckProduction he can’t
@ChiquitaSpeaks3 ай бұрын
@@matthewhue …wdym they just stated they watched a video?
@brennangleason59745 жыл бұрын
*Y O W Z A S*
@yohansaldana82185 жыл бұрын
What's that?
@yohansaldana82185 жыл бұрын
@@NodenGaming ???
@johnnyjoestar64785 жыл бұрын
christian Saldaña 11:22
@yohansaldana82185 жыл бұрын
Oooooohhhhhh...okay.
@egorovcharenko70145 жыл бұрын
Яуза ))) A river in Moscow!
@krukowstudios36865 жыл бұрын
Let's prove that the square root of 2 is irrational... BUT FIRST! What is a number?
@augusttyellis5 жыл бұрын
...and how much does a number weigh?
@BerlinWallNeverFall5 жыл бұрын
And where is it in time
@edwardwong95995 жыл бұрын
Can I eat it?
@emmatcr57835 жыл бұрын
It's odd to have even numbers..
@Burdarper5 жыл бұрын
... and how does it smell in space ?
@alicewilson19133 ай бұрын
learned this one in college, crazy what Euclid goes on to prove using irrational numbers, the icosahedron construction proof at the end is mindblowing
@-GamesNGames-11 ай бұрын
This is literally 8th-9th grade exact maths, he is teaching in such a way that its part of our dopamine dose. Amazing
@williewanker11874 жыл бұрын
'Unless our teachers have been lying to us our entire lives' "YoU wOn'T aLwAyS hAvE A cAlCuLaToR wItH yOu"
@mohiburrahman83313 жыл бұрын
Here most of the job related exams don't allow calculator imoooo 😭😭😭😭
@dewut4203 жыл бұрын
@@mohiburrahman8331 Practice maketh perfect
@mailbox39823 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.
@martingouws38763 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_Butters3 жыл бұрын
Well to be fair they didn’t lie, they just didn’t know
@lordonez37944 жыл бұрын
Me: Doesn’t like math Also me: watches man do math for 17 minutes
@haydenboyer91934 жыл бұрын
Can relate
@OGrupxe4 жыл бұрын
I mean, Michael somehow teaches way better than my math teacher. Don't know about you guys.
@keemo46474 жыл бұрын
@@williammay451 same
@marcel79224 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.
@fliiiou63884 жыл бұрын
I'm your 666th like, you're now the devil
@netslamders6803 Жыл бұрын
I remember watching this a couple years ago and not understanding a single thing. It feels good watching it today and understanding everything
@catmoon9511 ай бұрын
That's why I love maths. I think it's really interesting how you play with numbers to solve/prove things.
@YaDingus3 жыл бұрын
I wish someone would look at me the way Michael looks at the number 8.
@ProudlyIdiotic3 жыл бұрын
Oooh look at the beauty
@dvision42032 жыл бұрын
You’ll find them ☺️
@user-fw1bu6fd2i2 жыл бұрын
Sorry, I cannot keep looking at you. You are just too bright 😎
@flamingaish2 жыл бұрын
Lmfao
@monkeybusiness6735 жыл бұрын
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!!!!"
@m3morizesАй бұрын
7:31 I love how he underlines the numbers once for the odd numbers, and twice total for the even numbers. Almost poetic.
@noodlespoo10 ай бұрын
Some men love money. Some love the smell of napalm in the morning. But the truly scary ones love reduced fractions.
@anhhuynhkimnguyen67935 жыл бұрын
He protecc He attacc But most importantly, He bacc
@hussaina.44315 жыл бұрын
... on the wrong channel
@jtjs28905 жыл бұрын
Second comment
@frogenthusiast40175 жыл бұрын
@@jtjs2890 why u gotta announce that
@sorako045 жыл бұрын
VN :)))
@hoangao4375 жыл бұрын
Though Kevin and Jake are still active
@UnknowingNeko4 жыл бұрын
Did I ask for this? Absolutely not Did I need this? Absolutely not Did I love this? Absolutely
@SuperT4 жыл бұрын
Not
@rhymescheme11943 жыл бұрын
Did i need to tell this: Absolutely not Am i telling this: Absolutely I am your 111th like
@riooo80723 жыл бұрын
i needed this
@shinygreninja46503 жыл бұрын
@Modar Bilal01 but first let us see, what is need...
@realeyes81993 жыл бұрын
I needed this
@Alec0124 Жыл бұрын
Thanks for saying zero is an even number. This makes me happy
@arsenvokrug4198 Жыл бұрын
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!
@wow-wk4ww3 жыл бұрын
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 Жыл 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.
@Lemony12311 ай бұрын
@@henry497 I mean, A teacher cannot check all student at the same time.
@pearlphosphophyllite9954 жыл бұрын
Binomial Multiplication: *appears* Me: So we meet again...
@squibble3114 жыл бұрын
how did u americans not learn that (x+y)² = x²+2xy+y²
@pearlphosphophyllite9954 жыл бұрын
@@squibble311 No, I am not American, and yes, I did learn that.
@sanyalox014 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
@jacksonbrewer23803 жыл бұрын
sini harshan we did learn it. It’s not hard
@padmanabanraghavendran35703 жыл бұрын
@@jacksonbrewer2380 idk about western education (i heard it is slow) but asians learn basic algebra at 5th or 6th grade
@CrumBummin2 ай бұрын
I feel like math really gets Michael going. I could totally feel what I interpret to be his normal everyday cadence and voice slip out a few times in this vid, as opposed to his more calculated, mysterious, and scripted youtube voice. Perhaps this has been seen in other videos before and I've missed it, but this felt very humanized from the perspective of someone showing you math from a kitchen table sort of vibe.
@nancyzipperer8819Ай бұрын
I'm pretty sure this is the video that started Terrance Howard's suspicion
@mememem5 жыл бұрын
2:31 he says the thing
@Noah-gn5re5 жыл бұрын
What even is that pfp
@rexevan67145 жыл бұрын
ROLL THE 🎶
@Fassle5 жыл бұрын
it scares me
@fastandbulbous96975 жыл бұрын
I unironically want to kiss Cirno's ocks on your profile picture
@joshuaosei56285 жыл бұрын
Or did he?
@hayden38655 жыл бұрын
He draws "8" like I'm back in primary school
@hardscope85294 жыл бұрын
Yaaa thought the same.. xD
@st4ndby4 жыл бұрын
That irritated me so much 😄
@steelforge85774 жыл бұрын
@@williammay451 Or did you?
@keemo46474 жыл бұрын
@@steelforge8577 I mean what is writing (vsause music starts)
@elementneon2 ай бұрын
I never knew there were 2 different 8's until this video, a sideways infinity 8, and a snowman 8. His snowman 8 is much neater than my sideways infinity 8 so I may have to try adopting the snowman.
@looney1023 Жыл бұрын
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
@jjutt873 ай бұрын
/Terrence Howard has entered the chat
@NetroxSM5 жыл бұрын
Can we rename this channel to Vsauce4 - Mainly DONG and sometimes Original Vsauce
@dumbasgenius72275 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
@cosmiccreeper2475 жыл бұрын
Or just new vsauce 1 then rename vsauce 1 to vsauce premium
@fhz30625 жыл бұрын
This is Vsauce4 - Ponto em Comum (Made in Brazil): kzfaq.info/get/bejne/ZuBii92V1qexhoU.html It is an amazing documentary about vaccines. "Olá Criaturas da Internet, aqui quem fala é Davi Calazans." SAP: Hey Vsauce, Davi Calazans here.
@ZomBeeNature5 жыл бұрын
Maybe it's irrational because of a traumatic experience
@-_Nuke_-5 жыл бұрын
@@owltaku5757 xD
@barrackoli5 жыл бұрын
It saw 7 8 9
@bard1195 жыл бұрын
What if the number 2 identifies as a 3?
@MohamedHaizam8 ай бұрын
I Prove it like this Let √2 be rational i.e √2 can be expressed as a/b (were a and b are co-prime integers) √2 = a/b by squaring on both sides 2 = a^2/b^2 transposing b^2 to l.h.s 2.b^2 = a^2 therefore a^2 is divisible by 2 (if p^2 is divisible by a then p is also divisible by a) then a is also divisible by 2 now let a = 2c sub it in 2.b^2 = a^2 then we have 2.b^2 = (2c)^2 2.b^2 = 4.c^2 b^2 = (4.c^2)/2 b^2 = 2.c^2 therefore b^2 is divisible by 2 (if p^2 is divisible by a then p is also divisible by a) then b is also divisible by 2 now a and b have a common factor 2 this contradicts with the fact that a and b are co-prime integers therefore our assumption is wrong √2 is irrational Hence Proved.
@Gohas098 ай бұрын
I am in 10th grade and they taught me this in school
@MohamedHaizam8 ай бұрын
@@Gohas09 same here
@dustinpowell7353Күн бұрын
I love knowing the proof for multiplying fractions. This was so cool to watch.
@bricck5 жыл бұрын
15:40 "Oh my goodness gracious!" Lol. Getting so excited for an even number
@aleksandarvlasev40305 жыл бұрын
It's like he can't even
@bethmil7055 жыл бұрын
@@aleksandarvlasev4030 LOL
@mustafaali3333-q1m5 жыл бұрын
+Alexander Vlasev u made my day 😂
@plg28594 жыл бұрын
When you wake up on Monday and remember that you didn't do ur homework 0:13
@jordymottershead4 жыл бұрын
haha
@Schmlif60904 жыл бұрын
underrated
@DanS0444 жыл бұрын
I didn’t notice how he wiggled XD
@carsonmorris1274 жыл бұрын
Dan Slater woah I just noticed that
@rahimeozsoy42444 жыл бұрын
Oww....
@mohamedelzoheiry14133 ай бұрын
the solution of square root 2 in nearest fraction is 1871/1323 or 1970/1393 or 3124/2209 or 3363/2378 or 5234/3701 or 7105/5024 or 8119/5741 or 9611/6796 the solution of square root 2 is 25/18 + 1/42 + 1/660 = 19601/13860 = 1.4142136 1.4142136 = (2)^(1/2) the solution of square root 2 is 11/8 + 3/83 + 6/1955 = 1835819/1298120 = 1.4142136 1.4142136 = (2)^(1/2)
@hYro_Z Жыл бұрын
Okay, this is the best KZfaq Video I've ever seen. It's so simple, yet so beautiful and inspiring and I think this is, what makes it so good
@KyrieFortune4 жыл бұрын
Michael: writes 8 as two circles instead of a single interlocked line Everyone, while going through content aware scale: *YIKES*
@user-fs3ch6cc3j2 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
@Hugowtum2 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.
@noobeleman13ylonce692 жыл бұрын
yikes
@scibanana35422 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.
@traywor16152 жыл бұрын
What does it mean to be going through content aware scale?
@yikes67585 жыл бұрын
i wish my math teachers were as engaging as you, god damn
@Tor.G5 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.
@HeroRaze5 жыл бұрын
it's hard to get your students' eyes to zoom in on your face at comedic moments
@shinydewott5 жыл бұрын
Ryan G-P underrated comment
@jamesramirez04085 жыл бұрын
0:12
@DavidDias75 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
@carriersignal6 ай бұрын
Now if only my math instructors in school could have explained things as thoroughly and with such enthusiasm, instead of just glossing over everything.
@smoceany9478Ай бұрын
i think we would all be a lot better at math if we learned why things were true rather than that they were true, really gives you an understanding for the mechanisms on the inside. great video
@goodman95855 жыл бұрын
Wait, Michael writes 8 as one circle on top of another.
@lordelmo69595 жыл бұрын
Let him live in peace with his circle 8.
@BertGrink5 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.
@KenmoreChalfant5 жыл бұрын
THERE ARE DOZENS OF US
@utube42045 жыл бұрын
Normies
@eshan3095 жыл бұрын
Y O O O O W Z E R S
@goodman95855 жыл бұрын
Hey Vsauce, Michael here. Vsauce is my main channel Or is it? 🎵🎵🎵🎵🎵
@RAHISTILLL5 жыл бұрын
Hahaha I love this comment
@elementneon2 ай бұрын
I have never seen anyone write an 8 like that, but it is much neater looking that my sideways infinity 8.
@Woah93944 ай бұрын
And this proof works for the square root of any non perfect square numbers
@kennethirgendwas46165 жыл бұрын
This is kind of a fusion of numberfile and vsauce And for some reason it is on DONG
@youreyesarebleeding13683 жыл бұрын
God if every math teacher was like this everyone would have their Master's
@mikkihintikka72733 жыл бұрын
yeah like in 40 years
@Jack-do5tq3 жыл бұрын
@@mikkihintikka7273 lol
@padmanabanraghavendran35703 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
@mikkihintikka72733 жыл бұрын
@@padmanabanraghavendran3570 yep and they learn it in tenth of the time
@youreyesarebleeding13683 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
@AK-ct9pd3 ай бұрын
1x1=2
@z8ian3 ай бұрын
You're so funny 😂
@c_sea1n2 ай бұрын
x=2
@mildabrilproductions2143 ай бұрын
Someone send this to Terrence Howard
@Brotgl5 жыл бұрын
Michael: * says something * me : yes yes very good * stares intensely at t-shirt *
@saral98175 жыл бұрын
Hello reyan
@Brotgl5 жыл бұрын
close but no cigar ;-; anyway hi ¯\_(ツ)_/¯
@grandayy5 жыл бұрын
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!
@TheUltimateDavyGravy5 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
@Capstfu5 жыл бұрын
I thought we all knew that most even numbers have irrational square roots 🤷🏾♂️
@FlamingJ9995 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.
@jasonroyer98705 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
@FlamingJ9995 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.
@franciscoramos7391 Жыл бұрын
I can't believe I watched the whole video. This was surprisingly very entertaining. I wish my math teachers had been like him
@MrXeberdee3 ай бұрын
Tell Terrence Howard.
@bugjams5 жыл бұрын
Micheal: Do you know what an even and an odd number are? Me: I do! Micheal: ...or do you? Me: 😦😦😦
@sickomode27614 жыл бұрын
Alex Baldwin how did you spell it wrong twice
@bugjams4 жыл бұрын
@@sickomode2761 Micheal? That's how autocorrect tells me to spell it. :(
@mariafe70504 жыл бұрын
Alex Baldwin Can you turn off autocorrect?
@platypuschallenger4 жыл бұрын
Spelled 'Michael'
@sharkronical4 жыл бұрын
It's Mikál
@matthewtyburski76244 жыл бұрын
“Let’s prove that the square root of 2 is irrational” “Yay!” “But first, we have to reteach all of the math you learned in 1st grade”
@videogamemusic29624 жыл бұрын
“Yay?”
@Alfaris4 жыл бұрын
In 1st grade, they teach you how to do arithmetic. In this video, he teaches you why the arithmetic works. I guarantee you your teacher was not proving the arithmetic rules in 1st grade.
@ccspizza77784 жыл бұрын
Wait you did binomial multiplication in first grade
@generichomosapien46664 жыл бұрын
isn’t numbers just lines made by some evolved hairy apes used to count things so the mammals look cool?
@ajaybyadgi26724 жыл бұрын
yang ye also it's used for some other stuff somehow idk tho
@badilostykes10 ай бұрын
Learning more info from KZfaq in 17 minutes than my school can provide in an entire lesson, math edition
@dizzybee73862 ай бұрын
Vectors, scalars and quantities are like putting a ruler against the universe and expecting a graph.
@michaelbuckers5 жыл бұрын
Dong status: fully expanded.
@the711devin45 жыл бұрын
Channel name “Dong”: fully retracted.
@remlo54825 жыл бұрын
D!NG*
@add8525 жыл бұрын
Mandela Effect at it's finest
@FrozakRL4 жыл бұрын
Add 852 ??
@MrMan-np9jg4 жыл бұрын
@@remlo5482 r/woosh
@sujalgvs9874 жыл бұрын
Michael looking at 8 : *ahegao faces* Michael looking at 0.8: *incoherent screaming*
@DrumBum561Ай бұрын
Someone has to get Michael to draw his 8s another way, it’s driving me nuts
@jatinx2x7 ай бұрын
I love how the comments here are so calm and reasonable, meanwhile in vsauce it's pure chaos
@ythaenagor5 жыл бұрын
the way Michael writes the number 8 is mildly infuriating
@SuperTurtle05 жыл бұрын
Ethanagor S-D that’s how I write 8s
@alexandergeppert31745 жыл бұрын
@@SuperTurtle0 youre a bad person
@SuperTurtle05 жыл бұрын
Alexander Geppert not my fault I’ve always written them that way
@TotalImmort7l5 жыл бұрын
@@SuperTurtle0 style, eh?
@mrgraystripe13735 жыл бұрын
But it looks much better
@1lonestrider5 жыл бұрын
14:07 "Oh my goodness gracious" 15:40 "Oh my goodness gracious"
@ElCholoDeJolo5 жыл бұрын
Look at that. LOOK AT THAT
@rachaeljameson26415 жыл бұрын
look at what we have now!
@antonknittel35415 жыл бұрын
Thanks
@Dylan20579 Жыл бұрын
What is irrational is the way Michael draws the number 8
@MaxWright7 Жыл бұрын
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 Жыл бұрын
fr
@Adventurer-te8fl10 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.
@mudrams50153 жыл бұрын
Let’s just take a moment to appreciate how straight all of his lines are.
@oldmanjeffrey2 жыл бұрын
Those things were straighter than I am! But that’s not saying much.
@theAWPspammer2 жыл бұрын
@@oldmanjeffrey ayo
@ablemoo2 жыл бұрын
@@oldmanjeffrey 😏😏 okay daddy
@torin10065 жыл бұрын
I too enjoy binomial multiplication.
@DerpMuse5 жыл бұрын
as if theres any other kind
@MinecrafMobber5 жыл бұрын
it's all about polynomial multiplication
@jopegashira5 жыл бұрын
Think about remarkable products...
@TheV-Man5 жыл бұрын
Ah a fellow intellectual, I see.
@lily-vt8ic5 жыл бұрын
I do not. Especially when it involves exponets and 2 variables.
@user-vs2oe7rd5c10 ай бұрын
Vsauce saying "yikes" with the distortion filter just made me giggle
@haydenhuss8758 Жыл бұрын
When he proved it at the end, I was so excited that I pumped my fist and said, "Yes! We did it!"
@kjellandree74134 жыл бұрын
Vsauce: "atleast it isn't irrational" Me: "oh thank god" Vsauce: "or is it...?" Me: OH MY GOOOOD NOOOO
@Zephy9273 Жыл бұрын
Lol this was in our maths course class 10 of CBSE in India I’m surprised rest of the world isn’t taught this in school
@abir3299 Жыл бұрын
@@Zephy9273 Who said it isn't? It is taught in the UK.
@bighillraft Жыл бұрын
@@Zephy9273 Asians trying not to brag about their school systems (obviously making 6 year olds repeat the multiplication table 1000 times a day is a good way to teach, great work Asia)
@abhaypratap1085 Жыл бұрын
@Samridhi Pucha kisine ( who asked?)
@k_wl Жыл бұрын
@@bighillraft i am indian and literally every video of a hard problem i see some IIT dude is like "smh i did this problem when i was 11 give something harder", it annoys us too