Wau: The Most Amazing, Ancient, and Singular Number

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  • Опубліковано 26 січ 2025

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  • @SanketPatole
    @SanketPatole 5 років тому +3243

    Fun fact:
    All prime numbers are somehow divisible by Wau.
    Universal solution to the encryption problem.

    • @lox2404
      @lox2404 5 років тому +51

      Sanket Patole yes cuz wau is 1

    • @xzenplays3152
      @xzenplays3152 3 роки тому +96

      I don't know, maybe it's because Wau is equal to 1...

    • @themobiusfunction
      @themobiusfunction 3 роки тому +20

      @@xzenplays3152 Yes

    • @NerdWithLaptop
      @NerdWithLaptop 3 роки тому +31

      Correct. Have you ever seen e to the i tau = 1? That is the same as e to the 2i pi.

    • @NerdWithLaptop
      @NerdWithLaptop 3 роки тому +44

      And the reason a only a mathematician would call it a rectangle is because it's a square.

  • @freakanime5385
    @freakanime5385 5 років тому +3496

    E TO THE I TO THE E I O IS E TO THE WAU TO THE TAU WAU WAU
    i just love this part

  • @gogl0l386
    @gogl0l386 6 років тому +1977

    *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
      @silence439 5 років тому +66

      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
      @Sinus_Lebastian 5 років тому +107

      @@silence439 he knows what it is, that's why he made that joke

    • @HN-kr1nf
      @HN-kr1nf 5 років тому +9

      @@silence439 is nobody gonna do it?

    • @HN-kr1nf
      @HN-kr1nf 5 років тому +10

      @@silence439 absolutely nobody?

    • @HN-kr1nf
      @HN-kr1nf 5 років тому +9

      @@silence439 ok then

  • @Cory_Springer
    @Cory_Springer 6 років тому +2286

    It's been half a decade since I first heard of Wau, but I finally think I understand the complexities (and uniqueness) of this beautiful number!
    Wau is easily #1 on my list of favorite numbers.

  • @headrockbeats
    @headrockbeats 8 років тому +1234

    3:05 "Make the proportion Wau, and, well, you get something that most people wouldn't call a rectangle, unless you're a mathematician and being technical"
    I think this is the most clever line in the entire video. It's both deliciously misleading and absolutely true!

  • @treyforest2466
    @treyforest2466 6 років тому +1395

    “Oh hey, I remember this video, I watched it like four years ago. I remember it being full of really mind-boggling math.”
    ...
    “Oh, for fuck’s sake.”

    • @quantumgaming9180
      @quantumgaming9180 3 роки тому +165

      ME TOO. I've watched this video a few years ago and was just left baffled. I've come here back after years of high-school(in my last year) and I thought I got some pretty decent math knowledge to see if I understood at least a single concept or idea presented in this video. I still didn't get it, but after reading some comments here I realized that Wau is 1....

    • @EdbertWeisly
      @EdbertWeisly 3 роки тому +13

      SAME LMAO

    • @nwunder
      @nwunder 3 роки тому +112

      Vi really did prank millions of people over an entire decade with a single shitpost. it's beautiful

    • @Xayuap
      @Xayuap 3 роки тому +1

      ¿is this the ruining corner?

    • @AlvinBalvin321
      @AlvinBalvin321 3 роки тому +1

      SAME OMG

  • @Cyberspine
    @Cyberspine 8 років тому +4312

    Every prime is divisible by Wau.

    • @geoff7936
      @geoff7936 8 років тому +149

      For reals??

    • @khazalid4
      @khazalid4 8 років тому +228

      +Geoff Mulder yup. there is even more, wau/wau+ wau = 2 wau

    • @FourTwentyMagic
      @FourTwentyMagic 8 років тому +24

      then wau could be 0 too tho

    • @khazalid4
      @khazalid4 8 років тому +94

      Im not sure if you can divide by 0 even in situation like that. Can you?

    • @Cyberspine
      @Cyberspine 8 років тому +76

      Division by zero is undefined in regular math.

  • @LorenzoWTartari
    @LorenzoWTartari 2 роки тому +149

    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
      @MenacingBanjo Рік тому +5

      Spoiler alert!

    • @gdfyredragan2270
      @gdfyredragan2270 Рік тому +4

      the derivative statement makes no sense though, isn't a derivative of a constant just zero?

    • @LorenzoWTartari
      @LorenzoWTartari Рік тому +3

      ​@@gdfyredragan2270 i think she means the evaluation at 1 of the derivative of the exponential function rather than the derivative of e^1

    • @7takes
      @7takes Рік тому

      THIS EXACTLY OMG

    • @alguem24
      @alguem24 5 місяців тому

      e^(2iπ) was where I was like: "Wait what"

  • @rf7256
    @rf7256 7 років тому +2343

    But hau?

  • @the10000thspoon
    @the10000thspoon 8 років тому +1546

    "you get something most people wouldn't call a rectangle unless you're a mathematician" I laughed too hard

    • @alexbazzelle377
      @alexbazzelle377 7 років тому +31

      Mia V Whenever I read that I laughed, then said "wow." Probably just from reading/hearing it so much, but... Wow.

    • @themobiusfunction
      @themobiusfunction 3 роки тому +10

      Square!

    • @octobsession3061
      @octobsession3061 3 роки тому +8

      Well square is a rectangle, i'm trying being technical

  • @MicheleeiRettili
    @MicheleeiRettili 10 років тому +411

    The point of this video is that numbers with names like Pi, e, Golden Ratio etc. get so much love that the beauty of "normal" numbers like 1 get ignored. Give 1 a fancy name like Wau, and suddenly all its cool properties look a lot cooler. That's the point.

    • @MrLemonsChannel
      @MrLemonsChannel 10 років тому +27

      wau

    • @BambinaSaldana
      @BambinaSaldana 3 роки тому +9

      Wouldn't d/dx e^F be equal to 0 since e^F, if F=1, would be a constant, and not e?

    • @pranavkondapalli9306
      @pranavkondapalli9306 3 роки тому +3

      @@BambinaSaldana d/dx e^Fx = Fe^Fx
      close enough for a spoof video :P

    • @BambinaSaldana
      @BambinaSaldana 3 роки тому +1

      @@pranavkondapalli9306 Oh ok

    • @BambinaSaldana
      @BambinaSaldana 3 роки тому +2

      @@pranavkondapalli9306 They probably meant exp'(F), which is the derivative of e^x at F.

  • @damiannagel963
    @damiannagel963 6 років тому +997

    "every SINGLE flower and tree embodies Wau" I see what you did there

    • @drrigel63
      @drrigel63 5 років тому +59

      I feel personally attacked bc i watched this years ago and i didnt notice f=1 even tho it was obvious

    • @koruky
      @koruky 5 років тому +6

      Wau

    • @scottburgert9538
      @scottburgert9538 5 років тому +8

      @@drrigel63 Wau isn't a constant though 2:49

    • @drenzine
      @drenzine 3 роки тому

      @@scottburgert9538 how can u know

    • @drenzine
      @drenzine 3 роки тому +17

      UGH all the clues..
      0:56 "More than ONE way"
      1:30 Maybe a hint but the geometrical mean(which I think used in infinite fractions) is 1...
      2:35 You can just calculate it straight away.
      2:58 Log1 don't work so...
      3:14 Yeah it is what kids say "Square"
      4:15 It will be a point, like in the video
      4:35 Your example
      Edit: Also the title contains "Singular"

  • @Soogbad
    @Soogbad 6 років тому +1496

    Why was this not made on Waust of April?

  • @skyeturner5003
    @skyeturner5003 5 років тому +718

    I didn't quite realise what it was until e^2i*pi, then I thought, wait, that makes a lot of sense now.

    • @ItsAllEnzynes
      @ItsAllEnzynes 5 років тому +40

      Luke Diggle yeah that was the giveaway for me too :p

    • @limecyanizer4394
      @limecyanizer4394 5 років тому +18

      Then I went back to the beginning and did everything else.

    • @thomasokeeffe5050
      @thomasokeeffe5050 5 років тому +59

      Yeah that's where I got it as well. I was like wait just a goddamn second. I know my Euler's identity.

    • @green0563
      @green0563 5 років тому +3

      Same!

    • @generalgrievousjunior119
      @generalgrievousjunior119 5 років тому +2

      @@green0563 yep. I was suspicious then

  • @piotrdomagalski5096
    @piotrdomagalski5096 8 років тому +2168

    So matematicians really are able to troll people. Wau

    • @mariosstamoulis7345
      @mariosstamoulis7345 7 років тому +7

      +Ryan Park I think that I figured it out. clever. never noticed until now.

    • @MrJoshtheSuper
      @MrJoshtheSuper 6 років тому +10

      IBM Vrc yes, but it also happens to be true.

    • @dececanem
      @dececanem 6 років тому +1

      I'm confused?

    • @That_One_Guy...
      @That_One_Guy... 6 років тому +13

      wow is 1
      lol she got so many people

    • @lukahj
      @lukahj 5 років тому +3

      Well the first sum she was talking about she determines by Numberphile's dumb logic (i.e. that if a sum from 1 to k takes 2 values depending on whether k is odd or even, then if k tends towards infinity, she states that the number will be the arithmetic mean of those two numbers, which is incorrect, much like numberphile did in the 1 + 2 + .... = -1/12 video), so I'd say she is more of a dumb physicist than a mathematician

  • @hoid8069
    @hoid8069 2 роки тому +66

    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.

  • @geyjeanortiz4185
    @geyjeanortiz4185 6 років тому +2111

    Take a shot every time she says wau

    • @ErhanTezcan
      @ErhanTezcan 6 років тому +82

      I am be dieded

    • @TripNBallsGaming
      @TripNBallsGaming 5 років тому +77

      Are you trying to get people to die from alcohol poisoning?

    • @Sniffarn52
      @Sniffarn52 5 років тому +31

      You think anyone can afford that?

    • @eaoden8654
      @eaoden8654 5 років тому +21

      50 + Wau shots.
      Wow

    • @blakeb4583
      @blakeb4583 5 років тому +9

      Are you trying to kill us?

  • @capnkayso
    @capnkayso 7 років тому +840

    I'm surprised this wasn't uploaded on April wau :)

    • @skykopanek264
      @skykopanek264 7 років тому +37

      CapnKayso 823 April waust?

    • @MathNerd1729
      @MathNerd1729 7 років тому +1

      Exactly!

    • @OonHan
      @OonHan 6 років тому +1

      April 1

    • @Jo_Wick
      @Jo_Wick 6 років тому +1

      Same thing I was thinking.

    • @treyforest2466
      @treyforest2466 6 років тому +3

      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?

  • @terracottapie6872
    @terracottapie6872 8 років тому +409

    Another name for Wau is the Loneliest Number :-)
    P.S. I find out that Riemann's Zeta Function is undefined only for the value of Wau

    • @diegoostoja-kowalski5551
      @diegoostoja-kowalski5551 7 років тому +16

      Piotr Bienias I think you're wrong, there's also Wau to the Wau, e to the 2 pi Wau and many others, suspiciously containing Wau...

    • @jirawatnafung3900
      @jirawatnafung3900 6 років тому +4

      -1/12

    • @vin_fm2354
      @vin_fm2354 3 роки тому +3

      e^(i pi) = -1
      (e^(i pi))^2 = wau
      (-1)^2 = wau
      (-1)^2 = 1
      wau = 1
      Bruh.

    • @ordinaryshiba
      @ordinaryshiba 3 роки тому +2

      @@jirawatnafung3900 no, that's ζ(-1)

    • @Nick-lx4fo
      @Nick-lx4fo 3 роки тому +3

      Also interestingly, the natural log of Wau is 0

  • @scorpsjunknstuff4015
    @scorpsjunknstuff4015 5 років тому +519

    Everyonr talking about how wau is 1, but she did prove that the number 1 has infinite representations and and has alot of cool features.

    • @censacrof
      @censacrof 5 років тому +50

      I can prove every number has infinite representation: n=wau*n

    • @Deibler666
      @Deibler666 5 років тому +10

      0.999... = Wau

    • @asheep7797
      @asheep7797 3 роки тому

      1.0000000000... = Wau

    • @williamwilliam4944
      @williamwilliam4944 2 роки тому +2

      No, she didn't. She stated properties. Didn't prove them

    • @couldntcareless7884
      @couldntcareless7884 2 роки тому

      @@williamwilliam4944 they weren’t talking about proving properties, but showing that they exist and are cool.

  • @zzyzybynsky
    @zzyzybynsky 10 років тому +229

    Pretty surprised no one has mentioned this yet but (d/dx)(e^F) is not equal to Fe (where F is wau); the derivative of any constant with respect to "x" is 0, and e ≠ 0.

  • @dansam5462
    @dansam5462 6 років тому +1470

    I wonder if somebody didn't notice that wau is 1 and is now telling people about this ,"mágical number"

    • @LouisOnAir
      @LouisOnAir 6 років тому +152

      Dansam 546 me 6 years ago. 1/3 of my life has been a lie.

    • @justinxin8415
      @justinxin8415 6 років тому +15

      Def not me ;)

    • @johnadams-kf3my
      @johnadams-kf3my 6 років тому +59

      OOOOHHHH, I knew something was up. Got me good

    • @danielcox3983
      @danielcox3983 6 років тому +35

      I googled e^ pi*i and got 1 and was like "oh yeah lel"

    • @uzgarn-5121
      @uzgarn-5121 6 років тому +7

      Yeah lol

  • @Horrortelltales
    @Horrortelltales 8 років тому +1491

    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

  • @Simio_Da_Tundra
    @Simio_Da_Tundra 3 роки тому +64

    people tend to appreciate (and sometimes overly appreciate, imo) irrational numbers and their properties while ignoring those of the simplest natural numbers, great video!

  • @avanicole6700
    @avanicole6700 8 років тому +428

    Wau factorial is wau

    • @dlevi67
      @dlevi67 8 років тому +58

      Even more incredibly, (Wau - Wau)! = Wau.

    • @ZeroGD
      @ZeroGD 8 років тому +20

      and even, (Wau - Wau)! x Wau^3 = Wau

    • @grinreaperoftrolls7528
      @grinreaperoftrolls7528 8 років тому

      wau-wau=0 because wau=-1. e^ipi=wayu, so wau=-1.

    • @ZeroGD
      @ZeroGD 8 років тому +24

      Grin Reaper Of Trolls no, wau is 0.99999...

    • @dlevi67
      @dlevi67 8 років тому +2

      wau-wau = 0 for all finite values of wau. However she never said e^iπ=wau... she said e^2iπ = wau (2:40).

  • @freyamagna7351
    @freyamagna7351 8 років тому +613

    you motherfather XD
    this is the exact same case as calling water as dihydrogen monoxide and address its harmful properties in their harmful condition

    • @patrickhodson8715
      @patrickhodson8715 8 років тому +161

      Dihydrogen monoxide is a major component in acid rain, and yet is completely unregulated and makes its way into nearly all foods, even organic produce!

    • @GermanFreakPlays
      @GermanFreakPlays 8 років тому +53

      Patrick Hodson dihydrogen monoxide should be banned everywhere!!!

    • @fudgesauce
      @fudgesauce 8 років тому +84

      To make it more mathematical, you could say, "You mother factor!"

    • @pitreason
      @pitreason 8 років тому +79

      100% people who drinked dihydrogen monoxide have died

    • @arimago
      @arimago 8 років тому +28

      93%*

  • @Mark-ys1ce
    @Mark-ys1ce 8 років тому +328

    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, UA-cam 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
      @dlevi67 8 років тому +49

      Now all you need to do is to say this as fast as she does, and you're in business.

    • @patrickhodson8715
      @patrickhodson8715 8 років тому +36

      Everyone knows that e^(i*pi) + 1 = 0, but people often forget that e^(i*pi*wau + wut) + wau = wut as well.

    • @Merlin1908
      @Merlin1908 8 років тому +8

      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
      @queenbeatles12 7 років тому +5

      d/dx e^F=d/dx e^1=0, not equal to F.e

    • @splodinatekabloominate846
      @splodinatekabloominate846 7 років тому +1

      wut

  • @boston5814
    @boston5814 3 роки тому +69

    Wau is definitely one of the numbers in the world.

  • @xbzq
    @xbzq 7 років тому +250

    Wau is the loneliest number

  • @Nyocurio
    @Nyocurio 8 років тому +41

    The "log to the base of wau is like dividing by zero" got me. Because it can be expressed as ln(x) / ln(wau), and ln(1) = 0.

  • @QuinsonHonQBB123XX
    @QuinsonHonQBB123XX 8 років тому +604

    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
      @QuinsonHonQBB123XX 8 років тому +25

      Sort of, but I didn't get it.

    • @B0Boman
      @B0Boman 8 років тому +35

      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
      @dar0971 8 років тому +18

      dude
      once it got to powers I understood and started laughing

    • @KalikiDoom
      @KalikiDoom 8 років тому +10

      totally "Wau" it's just 1...

    • @TomFranklinX
      @TomFranklinX 8 років тому +3

      lol I knew it was 1 the moment I saw the first identity with the infinite fractal sequence 1/3

  • @markgearing
    @markgearing 5 років тому +441

    Dihydrogen monoxide is always bottled in multiples of Wau litres.

    • @TheLuckySpades
      @TheLuckySpades 5 років тому +38

      Tell that to my .33L bottle on my desk

    • @markgearing
      @markgearing 5 років тому +41

      TheLuckySpades - Okay.
      “Hey bottle, your capacity is Wau litres multiplied by 0.33”.

    • @TheLuckySpades
      @TheLuckySpades 5 років тому +6

      @@markgearing usually refering to multiples means integer multiples as otherwise every number is a multiple of every other (non 0) number since we are in a field.
      Multiples aren't that interesting in fields since multiplication in those behaves too nicely, so we usually stick to Rings like the integers

    • @markgearing
      @markgearing 5 років тому +38

      TheLuckySpades - You’re responding to a post about Dihydrogen Monoxide under a video about Wau and you’re expecting a sensible answer?
      Wau

    • @TheReligiousAtheists
      @TheReligiousAtheists 5 років тому +7

      Nah man, I only see hydrogen hydroxide everywhere

  • @igoryegin9531
    @igoryegin9531 9 років тому +425

    There is a famous pop band which is called "Wau Direction"

  • @debblez
    @debblez 6 років тому +857

    when you make an entire 5 minute shitpost about the number 1 disguised as "wau" and everyone buys it

  • @mheermance
    @mheermance 9 років тому +177

    Wau's other weird property is that it is neither a composite number nor a prime!

    • @GravelLeft
      @GravelLeft 9 років тому +33

      +Martin Heermance You might want to add: "And it's still a whole number", otherwise it wouldn't really be wierd xD sorry for being a smartass xD

    • @hhj4439
      @hhj4439 9 років тому +3

      +TheySmashedAnHourglass I know what you mean! hahahaha *feels akward because laughing at math joke nobody gets*

    • @vinayseth1114
      @vinayseth1114 9 років тому

      +Andi Cruz What's the joke? :/

    • @nirglazer5962
      @nirglazer5962 9 років тому

      +Vinay Seth it's just the number one.

    • @vinayseth1114
      @vinayseth1114 9 років тому

      +Nir Glazer No I know that. I was referring to the joke 'otherwise it wouldn't really be wierd'...I mean I didn't understand why that would be funny- different sense of humour here, I guess. :/

  • @gregkurzepa6319
    @gregkurzepa6319 5 років тому +165

    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
      @whythosenames 5 років тому +1

      Littleoak 12 only with numbers > 0 or do you mean the absolute value

    • @redshiftedlight205
      @redshiftedlight205 5 років тому

      @@whythosenames I think he meant the positive numbers, negative numbers it's just the reverse and zero stays the same

  • @Kabitu1
    @Kabitu1 8 років тому +161

    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
      @Spuntios 8 років тому +7

      +Kabitu1 great point kabituwau

    • @onecommunistboi
      @onecommunistboi 3 роки тому +8

      The Definition I learned in Algebra was "Numbers with exactly two factors". Sounds way cleaner, and still excludes wau.

    • @itismethatguy
      @itismethatguy Рік тому +1

      @@onecommunistboi wait you arent being serious right

    • @onecommunistboi
      @onecommunistboi Рік тому

      @@itismethatguy Im perfectly serious, wdym?

    • @alexandermcclure6185
      @alexandermcclure6185 10 місяців тому

      @@itismethatguy ... type e^(2i*pi) into Google and you might understand it all.

  • @anadice9489
    @anadice9489 9 років тому +293

    The "tau wau wau" part was lovely

    • @maartencuyvers6017
      @maartencuyvers6017 9 років тому +1

      +Anadice Brown Tau =2pi, look for the tau manifesto for more info

    • @anadice9489
      @anadice9489 9 років тому +3

      +IluveNightcore 4life I know, I just like how it all rhymed and was more onomatopoeia than an actual thing
      I mean, if wau was an actual variable, you wouldn't say wau wau, you'd say 2wau

    • @techy4198
      @techy4198 9 років тому +7

      +Anadice Brown wau wau is not 2wau. wau wau is wau^2.

    • @remy1337
      @remy1337 9 років тому +2

      +Anadice Brown yippie yaw yippie yae

  • @chleung6110
    @chleung6110 5 років тому +100

    I just spent 5 minutes to understand the number 1, thx for your video.

    • @imhostofyou
      @imhostofyou 2 роки тому

      А где вы видели такую единицу, что sin(F) = F - 1 ?

  • @janAlekantuwa
    @janAlekantuwa 8 років тому +550

    I realized what Wau was when Vi said that e^2ipi is wau.

    • @ZeroGD
      @ZeroGD 8 років тому +76

      Wau = 0.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999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99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999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999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...

    • @YourFriendtheGeek
      @YourFriendtheGeek 8 років тому +21

      I calculated some of the infinite fractions she was doing and got the answer every time. Thought I was doing something wrong, but...

    • @aidanhennessey5366
      @aidanhennessey5366 8 років тому +2

      lol same

    • @empirespythefirst
      @empirespythefirst 8 років тому +47

      I thought there was a character limit on comments....

    • @vicr123
      @vicr123 8 років тому +32

      I burned my finger on my phone screen trying to scroll down. _Thanks!_ :|

  • @linuslee6314
    @linuslee6314 9 років тому +79

    The most intellectual piece of trolling I have ever seen.

  • @nivedhrajesh6701
    @nivedhrajesh6701 8 років тому +462

    lol I'm a math major and only caught it at e^(2*i*pi)

    • @Steven-rj7wd
      @Steven-rj7wd 8 років тому +12

      Nivedh Rajesh but what about "but, this is wau times wau. It's all wau times wau." 2:00

    • @nivedhrajesh6701
      @nivedhrajesh6701 8 років тому +20

      I was too much in wau

    • @wojtek9395
      @wojtek9395 8 років тому +6

      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
      @paalkaaran 8 років тому

      haha obviously imaginary exponentiation is simply unit rotation

    • @wojtek9395
      @wojtek9395 8 років тому +1

      Haha, then people are brainless

  • @gavrilarazvan8888
    @gavrilarazvan8888 5 років тому +117

    I had wau - 1 girl friends

    • @CodecrafterArtemis
      @CodecrafterArtemis 5 років тому +16

      If you're having girl problems, I feel bad for you son, I've got 99 problems but a girl ain't wau.

    • @gavrilarazvan8888
      @gavrilarazvan8888 5 років тому +2

      Artemiy Solopov that was funny af

    • @youtubepooppismo5284
      @youtubepooppismo5284 5 років тому +1

      Man, i wrote the the same comment, SAME. and then figured out you wrote it first xD

    • @gavrilarazvan8888
      @gavrilarazvan8888 5 років тому

      UA-camPooppismo xD

    • @SaraBrownmusic
      @SaraBrownmusic 5 років тому

      UA-camPooppismo samee😂

  • @DekuStickGamer
    @DekuStickGamer 8 років тому +628

    Wau...Mathologer just trolled us.

    • @BrotherSquid
      @BrotherSquid 8 років тому +15

      umm... this is Vihart

    • @AlcyonEldara
      @AlcyonEldara 8 років тому +83

      Mathologer said in a video "go watch Vi Hart about Wau".
      I saw this video before, and I smiled when he said this ;)

    • @BrotherSquid
      @BrotherSquid 8 років тому +6

      oh lol i watch mathloger too I just never heard him say that before. What video did he say it in?

    • @nujuat
      @nujuat 8 років тому +6

      Same - and it's in Mathologers latest one (as of when I posted this)

    • @guiguspi
      @guiguspi 8 років тому +29

      Shit, I got trolled good. Only found out after reading this comment.

  • @theginginator1488
    @theginginator1488 7 років тому +361

    You can trigger people just starting to learn about primes by telling them that wau isn't prime

    • @axelpetersson5787
      @axelpetersson5787 7 років тому +1

      TheGinginator14 to teach them*

    • @someone4650
      @someone4650 6 років тому +14

      Wau is divisible by one and itself only, so it is prime

    • @someone4650
      @someone4650 6 років тому +5

      Michael Darrow r/woosh

    • @dcakmak
      @dcakmak 6 років тому +8

      Sarah Menkes it isnt prime at all

    • @TomasBruno-ww6tg
      @TomasBruno-ww6tg 6 років тому

      And you just demonstrated it

  • @alexpotts6520
    @alexpotts6520 8 років тому +57

    The trolling level in this video is over 9000 times wau.

  • @LogansDarling
    @LogansDarling 5 років тому +9

    2:45 is actually wrong. The derivative would equal 0, because it’s a constant.

  • @user-dx5wm1uz9d
    @user-dx5wm1uz9d 7 років тому +175

    any number bigger than zero raised to the 0th power is WAU

    • @awesomeminingwizard
      @awesomeminingwizard 6 років тому +17

      Štěpán Pospíšil some would argue 0^0=wau

    • @fengardice
      @fengardice 6 років тому +8

      Any number raised to the wau-1 is wau, including zero. (This is not a matter of debate.)

    • @ItsClint
      @ItsClint 6 років тому +11

      @Deito World ...

    • @hielcowestra1412
      @hielcowestra1412 6 років тому +13

      @Deito World r/woooosh

    • @theouxepl1222
      @theouxepl1222 6 років тому

      In fact 0^0 = wau too

  • @A_G_Benson
    @A_G_Benson 6 років тому +175

    "The simplest thought, like the concept of the number one,
    Has an elaborate logical underpinning.
    The brain has it's own language
    For testing the structure and consistency of the world." - Carl Sagan

    • @AlgyCuber
      @AlgyCuber 5 років тому +3

      CarlSagan42

    • @aaronmarks9366
      @aaronmarks9366 5 років тому +4

      Carl Sagan autotuned rap from 2009, anyone?

  • @rafemenon9578
    @rafemenon9578 7 років тому +213

    n/wau = n^wau

  • @ivysauberan4798
    @ivysauberan4798 6 років тому +62

    Gave it away with e^(2pi*i)

  • @cosinev1265
    @cosinev1265 6 років тому +448

    After more than 4 years of wondering what Wau actually is, I finally found out today.

    • @lechugasllimantm7268
      @lechugasllimantm7268 6 років тому +5

      but tell us

    • @xamzx9281
      @xamzx9281 6 років тому +5

      same omg

    • @oldcowbb
      @oldcowbb 6 років тому +23

      5:11 she give it away actually

    • @masrock9203
      @masrock9203 6 років тому +4

      I KNOW THIS IS FROM 8 MONTHS AGO BUT I WATCHED THIS VID SO LONG AND IT EQUALS 1????????? my childhood mind would have been blown

    • @obinator9065
      @obinator9065 6 років тому +9

      Masrock9 e^(2pi*i) already implied that. Since e^(pi*i) equals -1 you just go another 180 degrees further and arrive at 1.

  • @IWANTAWORLD
    @IWANTAWORLD 10 років тому +43

    how can this video not have been upleaded at Aprils first...?

    • @IWANTAWORLD
      @IWANTAWORLD 10 років тому

      moon tiger
      oohhhh,i get it. thanks

    • @thomaslatkowski9792
      @thomaslatkowski9792 9 років тому +4

      Cause it wasn't an April Fools joke. Everything she said was true.

    • @chetanphoenix
      @chetanphoenix 9 років тому +2

      moon tiger I feel so stupid..

    • @jacobthompson8477
      @jacobthompson8477 9 років тому +4

      April wau.

    • @starwarsjk99
      @starwarsjk99 9 років тому

      moon tiger That makes sense. The 5/6 + 5/6/6... can be rewritten as individual terms as 5/6 + 5/6^2 +5/6^3 ... which all ends up as 1.

  • @fyu1945
    @fyu1945 7 років тому +343

    I hate this girl so much because she's got a talent to just create a couple minute video and making me arguing it with myself for days.

    • @jjjx32
      @jjjx32 6 років тому +26

      Yeah one is a weird number

    • @Lady_Liliana67
      @Lady_Liliana67 6 років тому +2

      One is cool not weird

    • @oPunkko
      @oPunkko 5 років тому

      she’s just rambling about a weird number that has no use in the real world.
      A novelty.

  • @johnchessant3012
    @johnchessant3012 5 років тому +197

    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
      @alspezial2747 5 років тому +9

      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.

  • @Sam-tf9ip
    @Sam-tf9ip 9 років тому +78

    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
      @Sam-tf9ip 9 років тому

      Then*

    • @Sam-tf9ip
      @Sam-tf9ip 9 років тому +7

      jim speiser At the endish...

  • @julianlin6467
    @julianlin6467 7 років тому +27

    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
      @julianlin6467 7 років тому +2

      2:11 Not possible. No number can do that, based on simple mathematical rules. Oh wait. Wait. Wau.

    • @julianlin6467
      @julianlin6467 7 років тому +2

      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.

  • @nasekiller
    @nasekiller 8 років тому +306

    is there somewau who gets this?

  • @SliversRebuilt
    @SliversRebuilt 3 роки тому +28

    In computer science, wau is often taken to correspond to truth itself!

  • @humamsebai8604
    @humamsebai8604 8 років тому +134

    How long did it take each wau of you to figure how much Wau is

    • @patrickhodson8715
      @patrickhodson8715 8 років тому +43

      once she said e^i*2pi = wau
      Then I started the video over and realized how clever this video is lol

    • @scarfboy
      @scarfboy 8 років тому +6

      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
      @situationalhelpfulness3432 7 років тому +1

      literally 3 years

    • @JorgetePanete
      @JorgetePanete 7 років тому

      Humam Sebai the comments is how long

    • @mathcookie8224
      @mathcookie8224 7 років тому +2

      I found out at 2:07 with the infinite wau exponents

  • @Alexander-oh8ry
    @Alexander-oh8ry 6 років тому +786

    How to determine your IQ:
    Video Length in seconds minus the seconds until you realize what Wau exactly is

    • @masrock9203
      @masrock9203 6 років тому +193

      Alex ander so I watched this video like 3 years ago and just watched it again and realized, does that mean my IQ is (3*365*24*60*60)?
      update, I don’t know how to read apparently. my IQ is 318-(3*365*24*60*60) so basically I’m stupid

    • @Villfuk02
      @Villfuk02 6 років тому +34

      in that case i have 5 IQ :'(

    • @Alexander-oh8ry
      @Alexander-oh8ry 6 років тому +6

      I meant IQ = video duration in seconds minus seconds until realization

    • @Villfuk02
      @Villfuk02 6 років тому +1

      i know, that it should be the other way around, it was just a joke

    • @andrew7955
      @andrew7955 6 років тому +28

      0iq for me

  • @xchems117
    @xchems117 10 років тому +62

    This is Vihart's number 1 video.

    • @emilyblack7342
      @emilyblack7342 10 років тому +26

      Possibly a Spoiler...
      You mean her number Wau video :)

    • @omp199
      @omp199 10 років тому

      Emily Black This video was already spoilt by the title. If the title hadn't already given away what the number was, I wonder how long it would have taken me to twig what she was talking about...

    • @PrimusProductions
      @PrimusProductions 10 років тому +2

      Doggydog08 F is 15 in Hexadecimal...

  • @smorcrux426
    @smorcrux426 3 роки тому +11

    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

  • @heek40
    @heek40 8 років тому +285

    I like the way she says wau

  • @drawmafreak
    @drawmafreak 8 років тому +226

    all i can think about is that in german, wau is the sound that a dog makes.

    • @bacontf2
      @bacontf2 8 років тому +37

      dogs can speak german?!

    • @ShayerSUtsho
      @ShayerSUtsho 8 років тому +4

      German Shepherds, too...

    • @bacontf2
      @bacontf2 8 років тому +5

      S S Utsho Chowdhury no german shepherds go woof

    • @felixmausi
      @felixmausi 8 років тому +3

      bacon German shepards go wau wau

    • @bacontf2
      @bacontf2 8 років тому

      Felix Eberhardt no they go come by but in german

  • @belabertram
    @belabertram 8 років тому +1160

    e to the i to the e i o equals e to the wau to the tau wau wau

  • @Quwertyn007
    @Quwertyn007 5 років тому +17

    How is the derivative of e e? She's doing a derivative over x even though x is nowhere in the expression so it's just 0...

    • @zasharan2
      @zasharan2 3 роки тому +2

      They were trying to manipulate the derivative of e^x being e^x, but incorrectly substituted x as 1 inside the derivative, changing the meaning of the expression.

  • @elektronationz8033
    @elektronationz8033 6 років тому +176

    Is this April Wauth?

    • @soldeeznuts7831
      @soldeeznuts7831 6 років тому +15

      ElektroNationz no, but it's said as April the Waust.

    • @anonimouse5533
      @anonimouse5533 6 років тому +2

      Nope! This is actually all true.

  • @Yizak
    @Yizak 9 років тому +85

    This is such a troll video, but also very poetic! Good work!

    • @Yizak
      @Yizak 9 років тому

      ***** Well, have you Googled the number Wau?

    • @neekkhoue2457
      @neekkhoue2457 9 років тому +1

      Yikak4 It's not a real number... way (at lead in the context of the video) equals one

    • @marc_con_c2566
      @marc_con_c2566 9 років тому

      Yikak4 Here you have en.wikipedia.org/wiki/Digamma#Numeral

    • @Yizak
      @Yizak 9 років тому +1

      maor05 That's what I got too. But in the context of this video it's not six. Vi just took the Greek letter and assigned a different value to it.

    • @green4free
      @green4free 9 років тому

      in decimal it would be 0.9999999999999999999, nines forever

  • @i.c.stupidpeople4590
    @i.c.stupidpeople4590 8 років тому +137

    I realized what this is, when she said e to the 2i pi is wau. When it's actually just 1.

    • @piticea
      @piticea 8 років тому

      yeeeh

    • @chukkas9
      @chukkas9 8 років тому +2

      wau can be represented as one, but it's like the square root of 25 where its two numbers, 5 and -5

    • @izikblu
      @izikblu 8 років тому +1

      umm sqr root of a positive number is always positive

    • @chukkas9
      @chukkas9 8 років тому +9

      izikblu
      whats -5 * -5

    • @izikblu
      @izikblu 8 років тому +2

      Chukkas 25

  • @TheUKNutter
    @TheUKNutter 5 років тому +51

    I remember having the BIGGEST crush on Vihart as a kid.

    • @AniematedSteph
      @AniematedSteph 5 років тому +11

      Wau

    • @TheUKNutter
      @TheUKNutter 5 років тому +5

      M00NL0RD36 I was a strange 12 year old.

    • @Onnozelfilmpje
      @Onnozelfilmpje 5 років тому +4

      On vihart as a kid? Shame on you.

    • @TheUKNutter
      @TheUKNutter 5 років тому +6

      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
      @Onnozelfilmpje 5 років тому +4

      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.

  • @ThePirhana11
    @ThePirhana11 8 років тому +139

    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
      @CobaltYoshi27 8 років тому +34

      I thought the average of 2 and 1/2 is 1.25.

    • @ThePirhana11
      @ThePirhana11 8 років тому +7

      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
      @cdavid2200 8 років тому +5

      Pirans
      O means 0

    • @ThePirhana11
      @ThePirhana11 8 років тому +4

      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
      @blockbros9299 8 років тому

      Pirans proof that .999… doesn't equal 1: 9 doesn't equal 10

  • @JustAnothAznNPerson
    @JustAnothAznNPerson 8 років тому +187

    Waufu of the year

  • @JuiceBoxWizard
    @JuiceBoxWizard 8 років тому +85

    You played me like a damn fiddle!

    • @Metalhammer1993
      @Metalhammer1993 7 років тому +1

      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

  • @praveenb9048
    @praveenb9048 6 років тому +51

    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.

  • @StarTheTripleDevil
    @StarTheTripleDevil 7 років тому +702

    Vi: Are you a real mathematician?
    3 other people: Well, technically, nah.
    Vi: Have you ever caught an evil number, like a... like a real Pi?
    3 others: Nah nah.
    Vi: And no kind of usage of Tau?
    3 others: Nah.
    Vi: Alright, I can see, that I will have to teach you, how to be like Vi Hart.
    We are number Wau! Hey!
    We are number Wau!
    Now listen closely.
    Here's a little lesson in mathematics.
    This is going down in... uhh... UA-cam videos?
    If you wanna be a mathematician number Wau.
    You have to catch Pi and replace it with Tau.
    Just follow my moves and sneak around.
    Be careful not to make a sound.
    *one of the 3 people touches an apple pie*
    Vi: No, don't touch that.
    We are number Wau! Hey!
    We are number Wau! hey!
    Now look at this circle that I just found.
    When I say go, be ready to write its circumference.
    Go!
    3 others: 2πr
    Vi: Write it with Tau, not Pi!
    Ugh, let's try something else.
    Now watch and learn, here's the deal.
    We'll measure this right angle in radians.
    3 others: 1/2π
    Vi: What are you doing??
    We are number Wau! Hey!
    We are number Wau! Hey!
    Mathematician number Wau!
    We are number Wau! Hey!
    We are number Wau! Hey!
    We are number Wau!
    We are number Wau!
    We are number Wau!
    Hey! Hey!

  • @Chrnan6710
    @Chrnan6710 10 років тому +39

    Ϝ in decimal notation is 1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.................

    • @alexroodman4318
      @alexroodman4318 10 років тому +19

      0.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999...

    • @DeGuerre
      @DeGuerre 10 років тому +5

      Except that it also has other decimal representations, like 0.999999...

    • @siprus
      @siprus 10 років тому +3

      also 1.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.................1

    • @omp199
      @omp199 10 років тому +21

      siprus No.

    • @AwesomepianoTURTLES
      @AwesomepianoTURTLES 10 років тому +1

      *****
      Yea it does. Because 2 minus 0.999... = 1.0000000...1
      DUH!

  • @lenacui8089
    @lenacui8089 8 років тому +159

    this is wauderful

    • @cmb9173
      @cmb9173 8 років тому +42

      +Ϝ for the pun

    • @sthwrth3250
      @sthwrth3250 8 років тому +4

      wau,just wau,thats im supriawsed with this pun

  • @itays7774
    @itays7774 5 років тому +32

    Wau - Wau + Wau... = 1/2
    And, due to that we can conclude that Wau +2Wau + 3Wau +...=-1/12!!!!
    I really couldn't believe it, it's mind blowing!!!

    • @kairostimeYT
      @kairostimeYT 5 років тому +4

      I am sorry but both of the above identities are wrong.

    • @atomiccompiler9495
      @atomiccompiler9495 5 років тому

      THT Brickfilms we know wau is 1, but those identities are still wrong, I am a math graduate, I would be glad to explain them to you and in what sense they seem to be equal.

  • @groundg8397
    @groundg8397 8 років тому +27

    I don't even know what the heck she is talking about, I'm just enjoying that silky smooth voice of her.

    • @cdkumquat4953
      @cdkumquat4953 8 років тому +15

      +CaramelMacchiato The joke is that it's what happens when you take 1 and pretend it's a mystical number of the ancients.

    • @skycanth1969
      @skycanth1969 7 років тому +1

      CaramelMacchiato I never understand anything about what she's saying I just enjoy listening to her voice.

  • @tomtostadioom5593
    @tomtostadioom5593 7 років тому +208

    (Wau)/1 + (Wau)/4 + (Wau)/9 + (Wau)/16 ... = (π^2)/6

    • @BerfOfficial
      @BerfOfficial 6 років тому +13

      Tomato Stadium shouldnt the RHS be pi^(2*Wau)/6

    • @1e1001
      @1e1001 6 років тому

      Wau

    • @tf8896
      @tf8896 6 років тому +1

      Summation of function of (Wau)/n! From n=(Wau) to Infinity = e

    • @tomtostadioom5593
      @tomtostadioom5593 6 років тому +1

      How does this have 110 likes?

  • @dramawind
    @dramawind 8 років тому +108

    Waut the fuck did I just see...

    • @ZeroGD
      @ZeroGD 8 років тому +6

      wau are you asking me

    • @dramawind
      @dramawind 8 років тому +4

      ZeroGD Becwause.

    • @ZeroGD
      @ZeroGD 8 років тому +3

      Dramawind waull... okay then

    • @dramawind
      @dramawind 8 років тому +3

      ZeroGD I'm glwaud waue waunderstand each wauther.

    • @ZeroGD
      @ZeroGD 8 років тому +4

      Dramawind im prwautty glwaud too

  • @T0m1s
    @T0m1s 2 роки тому +18

    Fun fact: Wau is a palindrome, both mathematically and phonetically.

  • @maxsimes
    @maxsimes 6 років тому +48

    4:36 "wau is everywhere, every *single* tree or flower embodies wau"
    Haha i see what you did there

  • @joelhaggis5054
    @joelhaggis5054 8 років тому +57

    I'm surprised this wasn't uploaded on April 1st.

  • @chromdusw6428
    @chromdusw6428 9 років тому +41

    You should have uploaded this on April Wau!

    • @thepip3599
      @thepip3599 9 років тому +5

      That was an awesome comment.

    • @vicr123
      @vicr123 9 років тому +1

      April Wau... April Wau... Good joke :D

    • @MathNerd1729
      @MathNerd1729 7 років тому

      How did you know what I was thinking?

  • @shgysk8zer0
    @shgysk8zer0 3 роки тому +8

    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.

  • @jacobherlin3704
    @jacobherlin3704 10 років тому +28

    You're wrong about the derivative. Even if we didn't know it was 1, if wau is a number, the derivative of e^wau is 0 because that's just a constant.

    • @messyzephyr
      @messyzephyr 10 років тому +2

      That is a very good point I had missed. Cool.

    • @jacobherlin3704
      @jacobherlin3704 10 років тому

      messyzephyr It might have been just as impressive to say that the derivative of wau^x = wau*x

    • @j4yb1rd
      @j4yb1rd 10 років тому +4

      Jacob Herlin messyzephyr It was zero. The annotation corrected it to Fe-e^F.

    • @patrickscholl2484
      @patrickscholl2484 10 років тому

      Jacob Herlin It isn't, though.

    • @CruseCtrl
      @CruseCtrl 9 років тому +2

      She clearly meant d/dx(e^(wau*x)) = wau*(e^x), but just forgot the x

  • @alexkfridges
    @alexkfridges 9 років тому +56

    i was sucked in for a while, then you did e^2i pi
    :P

    • @thecubeur33
      @thecubeur33 9 років тому

      +SunBreaker Films Same lol

  • @thepip3599
    @thepip3599 9 років тому +48

    There really is more than one way to show Wau in decimal notation:
    1 and 0.999999999999999...

    • @thepip3599
      @thepip3599 9 років тому +1

      😉

    • @thepip3599
      @thepip3599 9 років тому +6

      Wait, as an infinite decimal? Oh, 1.00000000000000... All numbers are infinite decimals, kinda.

    • @msmsmsms8515
      @msmsmsms8515 9 років тому +11

      The Pip There are more than wau ways to show wau in decimal notation

    • @thepip3599
      @thepip3599 8 років тому

      +DERPALERT
      Ha!
      (I actually said that out loud. It was awkward. Like, just one "Ha". Not a full laugh. It was weird.)

  • @zealous919
    @zealous919 3 роки тому +16

    The derivative of e^1 is not equal to 1(e). It’s just a constant, so we send it to zero

  • @tikikcila
    @tikikcila 8 років тому +33

    I had to watch this a few times before I realized how hard I was being trolled.

    • @abadlydrawnsnowman1648
      @abadlydrawnsnowman1648 7 років тому

      nvm i was bing stupid

    • @qew89
      @qew89 7 років тому

      How stupid i was, at first I belived in this!!!

  • @TheRealFlenuan
    @TheRealFlenuan 9 років тому +25

    Let's officially designate January 1st as Wau Day!

  • @TheGreatNordini
    @TheGreatNordini 11 років тому +83

    Such number
    Very mystery
    So count
    Wau

  • @davidkaye821
    @davidkaye821 4 місяці тому

    The Algorithm served me up one of your videos, and I remembered this AWESOME video from a long time ago. And like most everyone else, I absolutely LOVED your math rhyme at 2:50, a truly SINGULAR performance! lol

  • @thepip3599
    @thepip3599 10 років тому +20

    Oh! She was actually talking about the number 1! That's so clever!

    • @DannyAditya-fm3nx
      @DannyAditya-fm3nx 2 дні тому +1

      Im reminding you of this video to remind you of this cool things!

    • @thepip3599
      @thepip3599 2 дні тому

      @ Interesting behaviour. Thanks though.

  • @NotQuiteFirst
    @NotQuiteFirst 10 років тому +73

    Almost Wau million views

    • @MilanMilan0000
      @MilanMilan0000 9 років тому +4

      The True Fizz ITS OVER WAU-THOUSANDS!!

  • @JeoshuaCollins
    @JeoshuaCollins 10 років тому +9

    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.

  • @alspezial2747
    @alspezial2747 5 років тому +12

    wau, i feel kinda stupid about how long it took to get it.

  • @firecarter319
    @firecarter319 6 років тому +22

    I saw the title, and I was like, it’s 0, isn’t it. Then I watched and I gradually was like, “oops, it’s one”