Wau: The Most Amazing, Ancient, and Singular Number
Рет қаралды 2,108,479
12 жыл бұрынWhat other amazing properties of Wau can you think of? Leave them in the comments.
My personal website, which you might like: vihart.com
@SanketPatole 5 жыл бұрын
Fun fact: All prime numbers are somehow divisible by Wau. Universal solution to the encryption problem.
@lox2404 4 жыл бұрын
Sanket Patole yes cuz wau is 1
@xzenplays3152 3 жыл бұрын
I don't know, maybe it's because Wau is equal to 1...
@themobiusfunction 2 жыл бұрын
@@xzenplays3152 Yes
@NerdWithLaptop 2 жыл бұрын
Correct. Have you ever seen e to the i tau = 1? That is the same as e to the 2i pi.
@NerdWithLaptop 2 жыл бұрын
And the reason a only a mathematician would call it a rectangle is because it's a square.
@freakanime5385 5 жыл бұрын
E TO THE I TO THE E I O IS E TO THE WAU TO THE TAU WAU WAU i just love this part
@DenimTornado2 4 жыл бұрын
i came on that moment...
@ijo-pali 4 жыл бұрын
Yeah, me too.t
@tenbillionfliescantbewrong9238 4 жыл бұрын
the derivative of e to the wau.
4 жыл бұрын
2:50
@demonking86420 4 жыл бұрын
This phrase + Vi's voice = My kokoro
@gogl0l386 5 жыл бұрын
*Wow* this must be one of the most complicated numbers ever. I heard an absurd proposal that suggested we should teach this as the first number to kids. Absurd.
@silence439 5 жыл бұрын
It already is. Did you know that any number divided by itself equals wau? you probably know what it is now, just reading this.
@Sinus_Lebastian 5 жыл бұрын
@@silence439 he knows what it is, that's why he made that joke
@HN-kr1nf 5 жыл бұрын
@@silence439 is nobody gonna do it?
@HN-kr1nf 5 жыл бұрын
@@silence439 absolutely nobody?
@HN-kr1nf 5 жыл бұрын
@@silence439 ok then
@rf7256 6 жыл бұрын
But hau?
@mambodog5322 6 жыл бұрын
wau is 1.
@elymajdou5668 5 жыл бұрын
Astonishing, Wau, just Wau!
@That_One_Guy... 5 жыл бұрын
2^wow = 2 log (wow) = 0 ^2 log 2 = wow sin 90 = wow cos 0 = wow tan 90 = not wow
@dirkdoogenstein 5 жыл бұрын
Mata Nui knows Hau
@RSPikachuAlpha 5 жыл бұрын
Mambodog 532 r/wooosh
@LorenzoWTartari 2 жыл бұрын
I remember watching this in highschool and being completely befuddled by the notion that such a number could even possibly exist, until i watched it again today, 5 years later after 3 years of studying pure mathematics because it just randomly appeared on my YT feed, and I'm a little ashamed to say ut took me 3 rewatches to finally figure out that she was talking about 1 lol
@MenacingBanjo Жыл бұрын
Spoiler alert!
@gdfyredragan2270 7 ай бұрын
the derivative statement makes no sense though, isn't a derivative of a constant just zero?
@LorenzoWTartari 7 ай бұрын
@@gdfyredragan2270 i think she means the evaluation at 1 of the derivative of the exponential function rather than the derivative of e^1
@7takes 7 ай бұрын
THIS EXACTLY OMG
@hoid8069 2 жыл бұрын
Fun fact: Around 100 years ago, when mathematicians were pondering the true essence of Wau, they said that it's like an empty box inside of another box. It turns out when you peel back all of the layers of this truly mystical number, all you're left with is nothing.
@MichaelDarrow-tr1mn Жыл бұрын
note: the box part of it is about set theory
@Simio_Da_Tundra 2 жыл бұрын
people tend to appreciate (and sometimes overly appreciate, imo) irrational numbers and their properties while ignoring those of the simplest natural numbers, great video!
@boston5814 2 жыл бұрын
Wau is definitely one of the numbers in the world.
@geyjeanortiz4185 5 жыл бұрын
Take a shot every time she says wau
@ErhanTezcan 5 жыл бұрын
I am be dieded
@TripNBallsGaming 5 жыл бұрын
Are you trying to get people to die from alcohol poisoning?
@humhmu508 5 жыл бұрын
dude you just killed me
@Sniffarn52 5 жыл бұрын
You think anyone can afford that?
@eaoden8654 5 жыл бұрын
50 + Wau shots. Wow
@QuinsonHonQBB123XX 8 жыл бұрын
I watched this 10 TIMES and I didn't have any clue what Vi is talking about. Then I looked at the comments and got pissed off.
@QuinsonHonQBB123XX 8 жыл бұрын
Sort of, but I didn't get it.
@B0Boman 8 жыл бұрын
Holy crap, I just watched the video again and now it all makes sense. I should have known at the first infinite product which oscillates between 1/2 and 2
@dar0971 8 жыл бұрын
dude once it got to powers I understood and started laughing
@KalikiDoom 7 жыл бұрын
totally "Wau" it's just 1...
@TomFranklinX 7 жыл бұрын
lol I knew it was 1 the moment I saw the first identity with the infinite fractal sequence 1/3
@chleung6110 5 жыл бұрын
I just spent 5 minutes to understand the number 1, thx for your video.
@imhostofyou 2 жыл бұрын
А где вы видели такую единицу, что sin(F) = F - 1 ?
@TheAgentJesus 2 жыл бұрын
In computer science, wau is often taken to correspond to truth itself!
@gavrilarazvan8888 5 жыл бұрын
I had wau - 1 girl friends
@CodecrafterArtemis 5 жыл бұрын
If you're having girl problems, I feel bad for you son, I've got 99 problems but a girl ain't wau.
@gavrilarazvan8888 5 жыл бұрын
Artemiy Solopov that was funny af
@youtubepooppismo5284 5 жыл бұрын
Man, i wrote the the same comment, SAME. and then figured out you wrote it first xD
@gavrilarazvan8888 5 жыл бұрын
KZfaqPooppismo xD
@SaraBrownmusic 4 жыл бұрын
KZfaqPooppismo samee😂
@T0m1s Жыл бұрын
Fun fact: Wau is a palindrome, both mathematically and phonetically.
@TheUKNutter 5 жыл бұрын
I remember having the BIGGEST crush on Vihart as a kid.
@AniematedSteph 5 жыл бұрын
Wau
@TheUKNutter 5 жыл бұрын
M00NL0RD36 I was a strange 12 year old.
@Onnozelfilmpje 5 жыл бұрын
On vihart as a kid? Shame on you.
@TheUKNutter 5 жыл бұрын
Peter N Wtf is wrong with you? If you think that was weird, I was 6 and told my mum that I wanted Carol Vordermann to be my wife.
@Onnozelfilmpje 5 жыл бұрын
Some people don't understand irony when it's staring them in the face :rolleyes: Don't get so triggered, it was just an intentional misunderstanding, a lame joke. Jeez.
@gregkurzepa6319 5 жыл бұрын
I heard if you multiply n by any number less than Wau it'll get smaller, and by any number greater than Wau it'll increase. Wau!
@whythosenames 5 жыл бұрын
Littleoak 12 only with numbers > 0 or do you mean the absolute value
@redshiftedlight205 5 жыл бұрын
@@whythosenames I think he meant the positive numbers, negative numbers it's just the reverse and zero stays the same
@capnkayso 7 жыл бұрын
I'm surprised this wasn't uploaded on April wau :)
@skykopanek264 6 жыл бұрын
CapnKayso 823 April waust?
@MathNerd1729 6 жыл бұрын
Exactly!
@OonHan 6 жыл бұрын
April 1
@Jo_Wick 6 жыл бұрын
Same thing I was thinking.
@treyforest2466 6 жыл бұрын
Shravan Only thing I don’t get was that calculus part. She said that d/dx e^wau = wau(e). But e^1 = e, so this is a constant function. Therefore shouldn’t the derivative be zero? Or am I supposed to assume that she meant e^x whenever she wrote e?
@ivysauberan4798 5 жыл бұрын
Gave it away with e^(2pi*i)
@feliperennt 5 жыл бұрын
me too
@hacker-7214 4 жыл бұрын
Yup lmao
@astro_penguin_ 5 ай бұрын
same
@praveenb9048 5 жыл бұрын
When you talked about e=mc^2, I had to check if the upload date wasn't 1st April by any chance. At that point I didn't know that wau=1. Then I read a comment where all was made clear.
@smorcrux426 2 жыл бұрын
I felt really smart that I figured out pretty early that she was talking about 1, but then what's going on at 2:48? the derivative of e is 0, not e
@Horrortelltales 7 жыл бұрын
2:50 e to i to the e, i O is the e to the wau to the tau wowow yippi yo yippi yey, all my dogs sing with me now bow wau wau yippi yo yippi yey
@chiara7069 6 жыл бұрын
SweDawgTv BOW WAU WAU
@tidteejitarlemitr2542 6 жыл бұрын
I LOVE IT
@electromorphous9567 6 жыл бұрын
Awesome 😂😂😂😂😂😂😂😂😂😂😂😂😂
@mynewaccount2361 6 жыл бұрын
2x speed. Thank me later
@omhekde9033 6 жыл бұрын
My New Account thanks
@johnchessant3012 5 жыл бұрын
I figured it out when you said that most people wouldn't call a rectangle with ratio wau as a rectangle. (It's a square.)
@alspezial2747 5 жыл бұрын
also the exponential thing is quiet obvious, although i need to admit that i still thought it could be a complex number or something weirder that i have no clue of.
@dansam5462 6 жыл бұрын
I wonder if somebody didn't notice that wau is 1 and is now telling people about this ,"mágical number"
@LouisOnAir 6 жыл бұрын
Dansam 546 me 6 years ago. 1/3 of my life has been a lie.
@justinxin8415 5 жыл бұрын
Def not me ;)
@johnadams-kf3my 5 жыл бұрын
OOOOHHHH, I knew something was up. Got me good
@danielcox3983 5 жыл бұрын
I googled e^ pi*i and got 1 and was like "oh yeah lel"
@uzgarn-5121 5 жыл бұрын
Yeah lol
@janAlekantuwa 7 жыл бұрын
I realized what Wau was when Vi said that e^2ipi is wau.
@ZeroGD 7 жыл бұрын
Wau = 0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999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9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999vv999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...
@YourFriendtheGeek 7 жыл бұрын
I calculated some of the infinite fractions she was doing and got the answer every time. Thought I was doing something wrong, but...
@aidanhennessey5366 7 жыл бұрын
lol same
@empirespythefirst 7 жыл бұрын
I thought there was a character limit on comments....
@vicr123 7 жыл бұрын
I burned my finger on my phone screen trying to scroll down. _Thanks!_ :|
@enelabe 4 жыл бұрын
2:49 people call it the "Old McDonald's theorem"
@alexandermcclure6185 3 ай бұрын
old macdonald had a calculator, e^i^ei0 and on that calculator he had a constant, e^i^ei0 with a wau wau here and a wau wau there here a wau, there a wau, everywhere a wau wau old macdonald had a calculator, e^i^ei0
@alexpotts6520 7 жыл бұрын
The trolling level in this video is over 9000 times wau.
@tunasayl2928 Жыл бұрын
Vihart,you're amazing. Thanks for making this kind of content.
@thepip3599 9 жыл бұрын
There really is more than one way to show Wau in decimal notation: 1 and 0.999999999999999...
@thepip3599 9 жыл бұрын
😉
@thepip3599 9 жыл бұрын
Wait, as an infinite decimal? Oh, 1.00000000000000... All numbers are infinite decimals, kinda.
@msmsmsms8515 9 жыл бұрын
The Pip There are more than wau ways to show wau in decimal notation
@thepip3599 8 жыл бұрын
+DERPALERT Ha! (I actually said that out loud. It was awkward. Like, just one "Ha". Not a full laugh. It was weird.)
@MrPassigo 8 ай бұрын
This video is a masterpiece. I love coming back to it.
@fghsgh 2 жыл бұрын
First time I saw this video, many years ago, I didn't get it. Now I do. It's beautiful.
@Kabitu1 8 жыл бұрын
Wau is so powerful it's actually been banned from a lot of mathematics. By every sensible definition wau should be a prime number, but because wau is so strange, that would make it part of every single numbers prime factors. Do you get how amazing that is, one number, which is a factor of every other number? Mathematicians couldn't handle this, it would make primes too chaotic, so they had to ban wau from the set of primes, and add this weird extra rule to the definition, so primes are today defined as "Numbers that are only divisible by themselves and 1, other than wau". I'm not making this up, that's the official definition in use today, people just often forget to mention that second part.
@Spuntios 8 жыл бұрын
+Kabitu1 great point kabituwau
@onecommunistboi 2 жыл бұрын
The Definition I learned in Algebra was "Numbers with exactly two factors". Sounds way cleaner, and still excludes wau.
@itismethatguy Жыл бұрын
@@onecommunistboi wait you arent being serious right
@onecommunistboi Жыл бұрын
@@itismethatguy Im perfectly serious, wdym?
@alexandermcclure6185 3 ай бұрын
@@itismethatguy ... type e^(2i*pi) into Google and you might understand it all.
@Mark-ys1ce 7 жыл бұрын
Reminds me of my favorite math fact. The number of divisors of any Prime Number is a Fibonacci number. Which is closely related to the fact that if you take any prime number, take it to the wauth power, and divide it by wau, you get a prime number. However, you missed a key part of Wau, which I shall call Wut. If you take Wau to the Wauth power and subtract Wau to the Wauth Root, you get Wut. Wut is the yin to Wao's yang. They are inexplicably linked. If you take Wau to the Wut and add Wut to the Wauth you get Wao to the Wut to the Wao. If you add Wut and Wao together and take the natural logarithm of that, then divide it by i, you get pi to the Wau minus Wut to the pi. That is just a taste though, KZfaq comments aren't well suited to fully exploring the relationship between Wut and Wao. Perhaps someone more familiar with Wut and Wao would care to elaborate.
@dlevi67 7 жыл бұрын
Now all you need to do is to say this as fast as she does, and you're in business.
@patrickhodson8715 7 жыл бұрын
Everyone knows that e^(i*pi) + 1 = 0, but people often forget that e^(i*pi*wau + wut) + wau = wut as well.
@Merlin1908 7 жыл бұрын
No, no, you shouldn't ADD Wut and Wau, the natural logarithm of that is just Wut. If you subtract Wau from Wut, then the natural logarithm of that has the properties you stated.
@queenbeatles12 7 жыл бұрын
d/dx e^F=d/dx e^1=0, not equal to F.e
@splodinatekabloominate846 6 жыл бұрын
wut
@fanimations.3609 5 жыл бұрын
Wau: The Most Amazing, Ancient, and Singular Number _Singular Number_ 1 wau = 1 I got fooled by the video before I found out the possible h i n t in the title that wau was equal to 1. Meaning, I went down to the comments after this video, thinking wau was something completely strange, then I found out wau is 1.
@shgysk8zer0 2 жыл бұрын
I saw this several years ago and couldn't comprehend what this number could be. Watched it again and considered an infinite fraction that is 2 or 1/2 at any finite step and what a reasonable answer would be at infinity. For the second infinite fraction, I noticed that the numerator was just a clone of F, so it's 5/6 + F/6 = F. Or, multiplying by 6, 5 + F = 6F -> 5 = 5F. So I missed it the Fth time and figured it out immediately the next.
@nasekiller 8 жыл бұрын
is there somewau who gets this?
@Asterixch99 8 жыл бұрын
she's talking about 1
@Willzp360 8 жыл бұрын
+Ich Bin Anonym *-1
@MetalMarauder 8 жыл бұрын
+Will Price no it's 1
@carterhrabrick8584 8 жыл бұрын
-Wau = infinity
@MetalMarauder 8 жыл бұрын
Carter Hrabrick no, -wau = -1
@Sam-tf9ip 8 жыл бұрын
I was really confused about her tone during the video, it sounded like she knew something we didn't. Thence got the troll.
@Sam-tf9ip 8 жыл бұрын
Then*
@Sam-tf9ip 8 жыл бұрын
jim speiser At the endish...
@SteveAcomb 2 жыл бұрын
Great video! Wau is an extremely underrated number with cosmic significance.
@zealous919 2 жыл бұрын
The derivative of e^1 is not equal to 1(e). It’s just a constant, so we send it to zero
@noskillman6507 2 жыл бұрын
THANKS
@alexandermcclure6185 3 ай бұрын
assume x = wau. thus, e^x = xe = wau e = e. read the dang annotations you doofus
@nivedhrajesh6701 7 жыл бұрын
lol I'm a math major and only caught it at e^(2*i*pi)
@Steven-rj7wd 7 жыл бұрын
Nivedh Rajesh but what about "but, this is wau times wau. It's all wau times wau." 2:00
@nivedhrajesh6701 7 жыл бұрын
I was too much in wau
@wojtek9395 7 жыл бұрын
Nivedh Rajesh since e^(pi*i)=-1 isnt e^(2*pi*i)=1 just because we turn 360 degrees from 1,0 to 1,0? I think this video is fake what do you think?
@paalkaaran 7 жыл бұрын
haha obviously imaginary exponentiation is simply unit rotation
@wojtek9395 7 жыл бұрын
Haha, then people are brainless
@addymant 2 жыл бұрын
For those curious, the fractal fraction can be solved algebraically. Set x equal to the denominator of the fraction. Because the denominator of the whole fraction is also the denominator of both fractions within the main denominator, x=3/x+1/x=4/x x^2=4 x=2 So 2/x=Wau
@swenji9113 2 жыл бұрын
If it was convergent then it would have to be 1, but the fraction does not converge so there is no limit, not even 1 nor wau
@phoquenahol7245 Жыл бұрын
So can the thing with the 5s and 6s. Let x be the fraction. Then 5/6+x/6 = x, x+5 = 6x, x = 1. This was the first dead givaway for me and the e^(2πi) and the thing about log base wau being undefined only confirmed my suspicions.
@alexandermcclure6185 3 ай бұрын
@@swenji9113 who's gonna tell him... Fine. Type e^(2i*pi) into google.
@PiercingSight 2 жыл бұрын
I haven't seen these videos in a long time. This is a good one for sure.
@chessandmathguy 5 жыл бұрын
Took me a while... Love it.
@gregzer 11 ай бұрын
Mathematicians really need to nerf Wau in the next update. Literally makes maining any other number futile
@sssilky3317 2 жыл бұрын
when I first watched this video I was a middle schooler who loved math, and I was like WOW this number is incredible but I don't understand it at all. and over the years I have thought about it a couple times, thinking "I've never heard of Wau anywhere else". Fast forward to today I'm a math major in college, and I saw this pop up in my recommended, and I finally realized that Wau is just one bruh :(
@julianlin6467 6 жыл бұрын
I realised Wau was probably 1, but I never thought someone would ever release a video to show us what the most everyday number can be when you don't know what it is. This applies to all of life! Honestly, you are awesome!
@julianlin6467 6 жыл бұрын
2:11 Not possible. No number can do that, based on simple mathematical rules. Oh wait. Wait. Wau.
@julianlin6467 6 жыл бұрын
TBH I never was fully sure it was 1 until I saw the comments, because I doubted anyone would do this. Well, other than you.
@MmadA-lg6ix 2 жыл бұрын
Fun fact: Even though Wau is considered (for all intents and purposes) a natural number, it is neither prime nor composite. Wau.
@connorconnor1631 2 жыл бұрын
is this just mathematical dihydrogen monoxide why must you bamboozle me like this
@SeanHarding-nv9li 5 күн бұрын
Dihydrogen Wauoxide
@jccusell 5 жыл бұрын
I was distracted by her extremely anying presentation and voice untill I dinally realized the value hahah well done!!!
@aleksandersabak 2 жыл бұрын
I don't get the one with the derivative. Wau and e are both constants, so shouldn't d/dx of e^wau be zero? I'm pretty sure that waue is not zero.
@lenacui8089 8 жыл бұрын
this is wauderful
@cmb9173 8 жыл бұрын
+Ϝ for the pun
@sthwrth3250 7 жыл бұрын
wau,just wau,thats im supriawsed with this pun
@BurgerSoda Жыл бұрын
Vihart continues to teach me more than math class.
@justfrankjustdank2538 4 ай бұрын
when i was 12 the sarcasm was entirely lost on me till 2 years ago i watched this again lol
@i.c.stupidpeople4590 8 жыл бұрын
I realized what this is, when she said e to the 2i pi is wau. When it's actually just 1.
@piticea 8 жыл бұрын
yeeeh
@chukkas9 8 жыл бұрын
wau can be represented as one, but it's like the square root of 25 where its two numbers, 5 and -5
@izikblu 8 жыл бұрын
umm sqr root of a positive number is always positive
@chukkas9 8 жыл бұрын
izikblu whats -5 * -5
@izikblu 8 жыл бұрын
Chukkas 25
@thepip3599 9 жыл бұрын
Oh! She was actually talking about the number 1! That's so clever!
@dannycastromusic_ 2 жыл бұрын
another property of wau is that it can make my bed, do my laundry, clean my house, vaccum my carpets, water my cacti, AND make delicious lasagna from scratch. truly a wonder of the universe.
@isaacpianos5208 2 жыл бұрын
I think my eyes just turned against each other and that crested a new feeling, similar to pain and confusion at the same time Great video, it's always good to learn new things
@JuiceBoxWizard 7 жыл бұрын
You played me like a damn fiddle!
@Metalhammer1993 6 жыл бұрын
happy i´m not the only one to my shame i needed to look at the comment section to get what was going on. just wau
@laureat7819 5 жыл бұрын
This is even better than ASMR. Wau
@merkdirwas 7 ай бұрын
come back after years - and i still love this wau
@IntelR 2 жыл бұрын
3 minutes and I realized that's just 1 with a fancy name, nice video!
@chromdusw6428 9 жыл бұрын
You should have uploaded this on April Wau!
@thepip3599 9 жыл бұрын
That was an awesome comment.
@vicr123 8 жыл бұрын
April Wau... April Wau... Good joke :D
@MathNerd1729 6 жыл бұрын
How did you know what I was thinking?
@JustAnothAznNPerson 7 жыл бұрын
Waufu of the year
@chedagoz7145 7 жыл бұрын
love me, Yuan-chan
@endothegreatthief4432 7 жыл бұрын
Wan Yuan PUNS
@kidyomu89 6 жыл бұрын
Wan Yuan noob I once got 300 likes
@ninstagram 2 жыл бұрын
This reminds me of the mock maths class we had at our first day of college
@humamsebai8604 7 жыл бұрын
How long did it take each wau of you to figure how much Wau is
@patrickhodson8715 7 жыл бұрын
once she said e^i*2pi = wau Then I started the video over and realized how clever this video is lol
@scarfboy 7 жыл бұрын
Was only vaguely suspicious of the 1/2 and 2 thing. Called it around e-i-2-pi like apparently quite a few. Reaaallly got more suspicious once she started getting silly :)
@situationalhelpfulness3432 6 жыл бұрын
literally 3 years
@JorgetePanete 6 жыл бұрын
Humam Sebai the comments is how long
@mathcookie8224 6 жыл бұрын
I found out at 2:07 with the infinite wau exponents
@sanujsrivastava4195 2 жыл бұрын
At some point, I began thinking wau is actually 1 but by the end of the video I dropped the idea
@yessir8248 5 жыл бұрын
youtube recommendations always leave me confused
@DannyDaDino Жыл бұрын
“The Most Amazing, Ancient, and SINGULAR number.” Goddamn it
@johnnye87 Жыл бұрын
Every time I watch this I notice a new detail i missed before. "Every SINGLE flower and tree you see embodies Wau..."
@okboing Жыл бұрын
holy- ok so i watched this *years* ago, and only now did it finally click what wau actually was
@toastyug 3 ай бұрын
When I first watched this video in elementary school, I was too young to understand the joke. I genuinely thought it was a cool number I had never heard before. But now I realize one is a cool number, a number I haven't been respecting and appreciating quite as much as I should be. Thank you Vihart
@Some_Guy77 2 жыл бұрын
This video is still good a decade later.
@maximusstorm1215 Жыл бұрын
This video is approved by Owen Wilson.
@gdwilliam2841 5 жыл бұрын
2:37 -2:54 **confused intensifies**
@ThePirhana11 7 жыл бұрын
How all of these work: - 1 also equals .9 repeating - That series equates to a fraction of n/n. Which is 1. - 1 multiplied and exponentiated to itself is always 1. - 1 to the power of of anything is 1, root n of 1 is always 1. - e^iπ is -1. e^2iπ is just 1. - d/dx e^1 is 0. e*1 and e^1 are both e. e-e=0. - I can't tell what she meant by "o" so I'm not doing anything about this one. - Logarithms can't work with 1.. Log1^4 wouldn't work since no amount of multiplying 1 by itself can get you to 4. This applies to all numbers except for 1. But Log1^1 pretty much gives you every number in existence. - You wouldn't call it a rectangle because it's a square. The fraction she gives is a fancy version of n/n. So 1. -It would have a degree of 1. It would collapse. - E^1/MC^2 = 1 is the same as saying E/MC^2: E=MC^2, E/MC^2 E^1/MC^2= 1^1 - If you kept putting one to the power of 1 is always one, putting n root of 1 is always 1. Meaning that 1^1 and Square Root 1 are always the same, hence why it wraps around.
@CobaltYoshi27 7 жыл бұрын
I thought the average of 2 and 1/2 is 1.25.
@ThePirhana11 7 жыл бұрын
CobaltYoshi27 lol oops, i guess i just spat that out. Youre right, feel free to explain why the series equals 1 if you like. :0
@cdavid2200 7 жыл бұрын
Pirans O means 0
@ThePirhana11 7 жыл бұрын
TGL SuperStarMan47 oh. okay then. So that problem with the 0 in it is essentially saying that e=e e^i^ei0= e^i^0= e^1= e e^1^(Tau)(1)(1) = e^1^Tau= e^1= e and as you know. e=e
@blockbros9299 7 жыл бұрын
Pirans proof that .999… doesn't equal 1: 9 doesn't equal 10
@joelhaggis5054 8 жыл бұрын
I'm surprised this wasn't uploaded on April 1st.
@joelhaggis5054 8 жыл бұрын
sorry , April waust.
@slightlokii3191 7 жыл бұрын
+Joel Haggis wau
@ianlucas6635 2 жыл бұрын
I'm confused, isn't the derivative of e^wau 0? or am I missing something.
@mattinsula7143 2 жыл бұрын
Wait, with the derivative of e^wau... what are you deriving with respect to? Wau is a constant isn't it?
@alexkfridges 8 жыл бұрын
i was sucked in for a while, then you did e^2i pi :P
@thecubeur33 8 жыл бұрын
+SunBreaker Films Same lol
@nwunder 2 жыл бұрын
So years after first seeing it, I came back to this video. While watching I had to double check that it wasn't an April fools video. Then I checked the comments, realized Wau was 1, and rewatched it and holy SHIT that video is incredible. Every little clever bit only gets funnier. The "more than one way to represent as an infinite decimal" is so good. That should have tipped me off to that meaning it's a finite decimal but it didn't. I didn't realize the rectangle was a square, for instance. The e^i*pi reference but she throws us off by mixing it up. Even a decade later this video was a profound experience. Thanks for coming to my TED talk.
@okramoffacebook1381 Жыл бұрын
7s this trying to express the passage of 3d as a 4d expression? (Writing and ongoing writing?
@ifroad33 5 жыл бұрын
Wow, I played around a little and found out this weird corrolation with the amount of parents I have. Dad hasn’t come back from the store yet. ;(
@tikikcila 8 жыл бұрын
I had to watch this a few times before I realized how hard I was being trolled.
@abadlydrawnsnowman1648 7 жыл бұрын
nvm i was bing stupid
@qew89 6 жыл бұрын
How stupid i was, at first I belived in this!!!
@mapledoctor3915 7 жыл бұрын
(sqrt(-wau))^(4 x wau) = wau
@slightlokii3191 7 жыл бұрын
i get it
@DonutKop 7 жыл бұрын
Yeah she doesn't seem to give any rigorous proofs to describe wau... only hard to follow factional logic with no real time to rigerously prove wau, we just have to take her word for it. I'd rather have numberphile or mothologer describe wau
@mapledoctor3915 7 жыл бұрын
DonutKop You do realize wau=1, right?
@DonutKop 7 жыл бұрын
Jacob H Yeah I did research And it does equal 1. Wonder why she doesn't say that outright though
@mapledoctor3915 7 жыл бұрын
DonutKop Because the video isn't meant to be serious.
@JackSmith-eb1ek 4 жыл бұрын
I didn’t get this till I watched it several years later and read the comments lmao
@royalninja2823 4 ай бұрын
I first found this channel and this video in middle school. I did not get the joke here AT ALL back then. Now I'm a few years into a math degree solving the little equations seeing how it all works out. Wau truly is an incredible number, isn't it?
@Hayernator 8 жыл бұрын
Pythagoras killed someone because of sqrt(2wau), who knew it was dangerous
@chessengineer837 8 жыл бұрын
+Hayernator2207 the cult is dangerous; the number itself, not
@kennyearthling7965 25 күн бұрын
Was this released on april 1st by any chance?
@adamjam5613 4 жыл бұрын
2:49 I mean the derivative of any value/expression (which excludes x) with respect to the x, equals zero since the slope of a tangent line for a straight line parallel to the OX axis is exactly zero for any x. therefore d(e^F)/dx=0
@SeanHarding-nv9li 5 күн бұрын
_d/dx (e^F)_ *does* equal _log(F)_, though...
@groundg8397 8 жыл бұрын
I don't even know what the heck she is talking about, I'm just enjoying that silky smooth voice of her.
@cdkumquat4953 8 жыл бұрын
+CaramelMacchiato The joke is that it's what happens when you take 1 and pretend it's a mystical number of the ancients.
@skycanth1969 7 жыл бұрын
CaramelMacchiato I never understand anything about what she's saying I just enjoy listening to her voice.
@itstagh1902 3 жыл бұрын
Im lowkey in love with your voice
@elektronationz8033 6 жыл бұрын
Is this April Wauth?
@soldeeznuts7831 6 жыл бұрын
ElektroNationz no, but it's said as April the Waust.
@anonimouse5533 6 жыл бұрын
Nope! This is actually all true.
@axbs4863 2 жыл бұрын
I love how it took me to the e^2ipi part to realize it was just 1 xD
@arthurmatematica 8 жыл бұрын
I can't believe this vídeo has more than wau million views
@WalterKingstone 8 жыл бұрын
+Arthur Caixeta Wau doesn't equal 1...
@arthurmatematica 8 жыл бұрын
+Walter Kingstone I don't remember me saying that :x
@WalterKingstone 8 жыл бұрын
Arthur Caixeta But the only amount of million views this video has more of is 1
@arthurmatematica 8 жыл бұрын
Walter Kingstone I highly disagree with your statement :P
@WalterKingstone 8 жыл бұрын
Arthur Caixeta How do you know that this video has more than Wau million views?
@ryannickelsen460 10 жыл бұрын
this is my property of wau that i came up with: wau=wau
@Banchaaa 10 жыл бұрын
That is so... stupid. Whatever. It's true.
@freshbeans2 4 жыл бұрын
The most awkward situation is making 60 cookies while watching the tau wau wau part and having to poop
@schroeder7483 2 жыл бұрын
My mind is blown. Wau sure is one... it's one... crazy number!
@JeoshuaCollins 9 жыл бұрын
2:49 "e to the i to the e, i , o is e to the wau to the tau-wau-wau" I almost died laughing, cause her voice tells me that it took her a couple of takes to say this part without breaking out laughing.
@conormcgreevy3195 Жыл бұрын
One mistake. 2:49, d/dx e^wau doesn't equal wau e, but it does equal (wau+wau)*(wau-wau)
@quashawnchadwick2334 2 жыл бұрын
The video is so zen. Like, “if you seek the wau, you will not find it. If you desire the wau, you can never have it. If you teach the wau, it is not the true wau. The wau can only be obtained by those who let go of desire, and open themselves to all of it.”
@NotQuiteFirst 9 жыл бұрын
Almost Wau million views
@MilanTheAngel 9 жыл бұрын
The True Fizz ITS OVER WAU-THOUSANDS!!
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