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Bill Payment Win


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Originally by XKCD

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» 619 Failures in Communication

  1. Søren H says:

    Good luck with that one!

  2. Mookie says:

    I pay all of my bills with imaginary numbers.

  3. Rogger says:

    haha the maths below is wrong…. its actually e^(i pi) which is equal to negative -1
    so the check is made out for 0.002 – 1 + 1 = 0.002 dollars

  4. i am a pretty snowflake says:

    [0.002+e^(2pie)] = 535.4936555 and the limit of the sum of (1/2^n) as n goes to infinity is I am a pretty snowflake.

  5. Jay says:

    Handwriting fail, on second thought, can’t determine if it is an i or a 2. =P

  6. Maxwell says:

    e^(i*Pi)=cos(Pi)+i*sin(Pi)=-1
    0.002-1+1=0.002 dollars for the bill
    Just another Failblog’s fail.

  7. knugu says:

    ffyyyyy omgshitzlolor —— hahahahah funny

  8. knugu says:

    sorry about that. but anyways, doeas it relly matter if it is a mathematicla error. i mean srsly you guys. as long as he’s not …. ooooh shiny

  9. Connor says:

    I’d call this one a ‘fail’ – pie=/=pi, and it’s Exp[Pi*i], not Exp[2Pi], which evaluates out to $.002. It’s a check for two cents, not $536.49

    • Huggy Bear says:

      yes, this has alredy been discussed, also some people are really blind

    • MadMax says:

      It’s a check for 0.2 cents, not 2 cents. And that’s exactly what makes this picture funny.

    • kannadzuki says:

      My .002 cents: In my (first-hand) experience, a few companies are very good about responding coherently and making sure their customers are happy (suppliers/dealers sometimes lose out, though), but by far, the majority of companies whose CS work I’ve seen done were usually disorganised, disjointed (communicating badly, or not at all, to CSRs), and sometimes even just out-and-out corrupt. Though there will always be a handful of bright, talented CSR staff who pay attention and are willing to question things (until ISO standards break their spirits)… most will just listlessly go with whatever they are told, and a few probably shouldn’t be trusted with the very little power they’re given. This Verizon nonsense was clearly a case of bad manuals (and probably bad training literature– which incidentally is often not updated when rep manuals are, based on what I’ve seen). And hence:

      (By now this issue should have long since been fixed, though.)

    • Eldon says:

      or .2 cents, depending if you ask a sane person or some finance guy at verizon

    • kim says:

      I’m with him on this one, you can’t call it a win if you can’t spell pi

  10. nosgoroth says:

    Randall, get out of my banking system!

  11. Captain Blah says:

    Bored now.

  12. Bruutaan says:

    if it’s the same guy who had the verizon math fail it would make cents for it to be written out for $.002

  13. Aja says:

    Sucky sucky only e^(2\pi i) dolla.

  14. Guusuu says:

    Fail!
    e^(i*pi) = -1, so total sum = $0.002, not $536.49.

  15. Phlip says:

    Rather old but still epic win on the part of Randall… Very fail on the part of the idiot who added the calculation.

  16. g4drake says:

    solve that verizon, i dare you, i double dare you

  17. Pro says:

    this will spice up my training for the math exam :)

  18. canread says:

    The biggest fail here is the description. First of all, it’s obviously an i because e to the i pi is negative one, or they would put it, e to the i pie is equals negative one have a nice day.

  19. Pro says:

    Oh, and why is the sum to infinity from 1/2^n = 1?

    • Aja says:

      1/2+1/4+1/8+… = x
      2*(1/2+1/4+1/8+…) = 1+1/2+1/4+1/8+…=x+1
      2x=x+1
      x=1

      • gnaa says:

        i dont think this is something you could call an correct argument. sorry but it kinda fails.

        • Aja says:

          Let K be a field.
          Then, for every element a of K, and every natural number n,
          (a-1)(1+a+a^2+…+a^(n-1)) = a^n-1
          You really want me to continue?

          • czuhc says:

            *onder de indruk*

          • gnaa says:

            let me think a little … but now i think i know what you want to say me. but if you continue and show how this is gonna work here, i guess it would be much easier. but without knowing this little helper, i guess everyone would think that this arguement is kinda recursive ^^

        • czuhc says:

          I would reserve that particular phrase for when your (imaginary) wife says: “Not now, gnaa, I have a headache”.

        • ralphie says:

          Ah, so you are a constructivist, a la Brouwer, and you do not allow for actual infinities. I see.

      • Gustav says:

        Is that a valid recursive proof? Kinda neat if so.

        • bore says:

          Let’s spell this out

          Define
          S = sum n=1 to infinity r^n.

          Then we split the sum into two:
          S = r + sum n=2 to infinity r^n

          Then write n=m+1
          S = r + sum m=1 to infinity r^(m+1)

          Factor out the r:
          S = r + sum m=1 to infinity r*r^m
          S = r + r*sum m=1 to infinity r^m

          Notice that we have S reappear on the right:
          S = r + r*S

          Rearrange:
          S – r*S = r

          Factor:
          S(1-r) = r

          Divide through by 1-r:
          S = r/(1-r)

          Set r = 0.5
          S = 0.5/(1-0.5) = 1

          We also need to worry about convergence. So this is only valid for when the magnitude of r is less than one.

    • Steven says:

      It isn’t

      S1 = 1
      S2 = 1 + 1/2 = 3/2
      S3 = 1 + 1/2 + 1/4 = 7/4
      S4 = 1 + 1/2 + 1/4 + 1/8 = 15/8

      It is clear what the pattern is: the n-th partial sum is

      Sn = 2 – 1/2^n

      If we do limit n -> infinity, we get Sn=2-0=2.

    • syn says:

      1/2^n = (1/2)^n
      Since the series runs from 1 to infinity,
      the first term, a = (1/2)^1 = 1/2
      the common ratio, r = 1/2

      Geometric sum to infinity = a/(1-r) = (1/2)/(1-1/2) = 1/2 * 2 = 1.

  20. Madam Meow says:

    Total win! I would have loved to see the look on Verizon’s A/R ladys face when she took that one out of the envelope. lol

  21. doublebanker says:

    I’ll cash it for ya….

    Daily gif blog

    DB

  22. Kane says:

    Math Fail…
    e^(i * pi), not (2 * pi).
    (The most beautiful equation in the world e^(i * pi) +1 = 0 ;D)

    So 0,002 + (-1) + 1 = 0,002

    The Sum of 1/2^n to infinity is 1 because

    1/2 + 1/4 + 1/8 + 1/16 ….. = ~1

    • jazzmoth says:

      It’s actually exactly 1. Crazy, right?!

      • TOM says:

        no, it’s close but it never reaches 1.

        • Aja says:

          In general, 1+x+x^2+x^3+…=1/(1-x)
          So in a sense 1-1+1-1+1-1+…=1/2

          • Spudd86 says:

            NO FAIL!

            that sum is undefined

            sums as you describe above always diverge for x>=1
            so no it is not true in general that
            1+x+x^2+… = 1/(1-x)

            it is however true for |x|<=1

          • Tom says:

            “In general, 1+x+x^2+x^3+…=1/(1-x)
            So in a sense 1-1+1-1+1-1+…=1/2″

            No.

            You’ve described an alternating series, not every series converges (for example your specific case.) The alternating terms are not monotonic (strictly increasing or decreasing and tending toward zero.)

            Something like 1 – 1/2 + 1/3 – 1/4 + 1/5 …. does converge because when you look at the alternating terms
            1 + 1/3 + 1/5
            and
            -1/2 -1/4 – 1/6
            both are monotonic, which is sufficient for the entire series to converge.

          • Brian Sherson says:

            That only works when |x| is strictly less than 1.

        • csdx says:

          actually since it goes to infinity it does equal exactly 1.
          And remember folks .9 repeating = 1

        • Brian Sherson says:

          Tom, if you only add up a finite number of the terms in the sequence, it will never equal one. But when referring to infinite sums, it is actually defined to be the limit. Not actual values of the series.

          So the infinite sum is one because the limit is 1, not having anything to do with what values you get when you stop at some point in the sequence.

  23. Haxored says:

    First!!!!!!!!!!!!!!
    Oh, w8,
    number f@il. :(

  24. The Random says:

    Good on ya mate.

  25. orion says:

    check win, failblog failest of all fails. The text below the picture is so wrong my eyes hurt. It’s check for 0.002.

  26. Fail says:

    Pi spelling fail?

  27. kolli says:

    Please stop the discussion. Study math first. It’s an “i”. The letter “i”. The one that comes after “h” in the alphabet. And in math the “i” stands for the imaginary unit of the complex numbers.

    There’s the large version of the picture, if you don’t believe that it’s an “i”:
    http://xkcd.com/verizon/

    It’s clearly “i”, the imaginary unit. e^(i * Pi) = -1, the sum gives +1. So the complex term and the sum are canceling out. What stays? Right the 0.002$.

  28. Malicite says:

    Math sucks.

  29. martie says:

    actualle the sum of 1/2^n is 0 so there was a fail in the explination ^^

    • Liquid_Fire says:

      There is a fail in the explanation, but that’s not it. You are wrong.

    • NM Gyrl says:

      There is certainly a fail in the explanation, but that isn’t it.

      > actualle [sic] the sum of 1/2^n is 0

      Think about it: you’re adding up a sequence of numbers that are all greater than 0 – even the teeny ones way out there where n is approaching infinity. Their sum *can’t* be 0. Numeracy fail …

    • Nylund says:

      I think you’ve confused taking the limit as n goes to infinity with taking the limit of the sum from n=1 to infinity.

      Had he written “lim n ->infinity 1/2^n, you’d be right as that’d leave us with 1/infinity which is indeed zero, but that is not what he wrote on the check. He wrote Sum n=1 to infinity, 1/2^n, which, as pointed out many times here is indeed 1. (how could an infinite sum of strictly positive numbers ever NOT be strictly positive?)

      And anyone who even thought for a second that it was a 2 and not an i is obviously not a math nerd. Euler’s identity is one of the most profoundly beautiful things in math as it so neatly relates pi, e, i, 1, and 0 in one simple and elegant statement. Think about it…something as weird as the concept as the imaginary unit on the complex plane, two immensely important, yet never-ending irrational numbers, and 1, the most basic integer all relate in such a way as to equal zero. Its like finding out that if you cross-breed a scorpion, an ostrich, a dragon, and a llama, you get a kitten.

      It is the type of thing math nerds get tattoos of:

      http://talklikeaphysicist.com/2009/black-ink-tattoo-euler-identity/

      http://talklikeaphysicist.com/2008/tuesday-tattoos-euler-identity-mathphysics-tattoo/

  30. ozymandias says:

    The real fail is the caption at the bottom where the math is wrong. The *real* amount is for $.002

  31. BratPAQ says:

    is this in dollar or in cents? oh wait, its verizon, it doesnt matter if its dollar or cents.

  32. Matt J says:

    too bad that isn’t the limit – the big Greek Sigma is SUM…
    however, the math is correct. I think that someone is finally putting his high school algebra skills to good use!

  33. papajon says:

    Not much of a win IMHO. No “person” billed him for 2 cents, it’s all computer generated. So what, you’re showing up a computer? Big whoop.

  34. Spiffy says:

    I went to high school with this guy. He is a douchebag. But XKCD is funny.

  35. rekkataichou says:

    XKCD = FAIL?

    MY WORLD JUST GOT TURNED UPSIDE DOWN!

  36. dannogranno says:

    Anyone who would trust the math skills of someone who writes Pi as “pie” has failed as far as I’m concerned.

  37. munineye says:

    This may be the best win in the history of Failblog. And for the record, if this is actually done by the guy from xkcd, my little nerd girl brain has just exploded and gone to heaven.

  38. Spotpuff says:

    As others have commented this is an epic math fail. Whoever did the caption needs to learn high school math.

    • mr. cuddles says:

      Actually, that’s Calculus, which is taught in college.

      • jazzmoth says:

        Unless you are smart, in which case it’s taught in high school.

        • mr. cuddles says:

          Hey dipshit, how about you blow me. I graduated in the top 10% of my class with a 4.58 GPA and I didn’t take Calculus until I was in college. And I was a math major. So you can go kill yourself now.

          • czuhc says:

            Wow, for a moment there it looked as if your avatar turned red and showed a lot of pointy teeth!

            • WhatIKnow says:

              I just giggled for about 10 minutes at the
              “Hey dipshit, how about you blow me.”

            • mr. cuddles says:

              The picture may be a little too far away, but I was also foaming at the mouth.

              • Sandi says:

                Hehe – we learned calculus in high school but it was a selective subject in our final year. Didn’t have to be smart to learn it, just had to select it as one of your subjects.
                Btw – how do GPA’s work where you are from Mr. Cuddles? Ours range from 0-9.

              • Calc? says:

                Umm, Exp[i*pi] = -1 is not really calculus… Neither is spelling pi correctly

              • Mr. Melvin says:

                My brother took calculus in high school, actually both of them… oh wait, I did too, you obviously just went to a shitty high school.

          • funnyguy25 says:

            last time i checked, you can’t get higher than a 4.0 GPA. I’m calling shenanigans on that.

      • The Moomin says:

        *squeeze*
        Nah, Calculus is the professor with the little beard and the teeny hat from Tintin. This is some kind of weird sum stuff.

  39. dk2008 says:

    Somebody’s getting his cell phone service canceled…

  40. nata says:

    i like how he spelled pi wrong

  41. anonymous says:

    this has to be the guy from the verizon operator argument. more power to ya.

  42. Eric says:

    My favorite part is that obviously Verizon meant $0.02.

    Since the check is for $0.002, he’s going to end up paying more late fees.

    Also, there is NO LIMIT anywhere. It’s a sum. The limit is redundant and unnecessary because the sum exists for n = infinity and all integers from 1 to infinity.

    Also, it’s i. Stop being retarded.

    0.002 + (-1) + 1 = 0.002

    -Eric

  43. anonym says:

    Why “Bill Payment Win”? The “winner” was blind.
    Already mentioned for 3933923 times, but here it is again:
    0.002 – 1 + 1 = 0.002…
    He was so near with $535.4936555

    i’m proud to be european.
    Bloody idiots.

  44. tz says:

    Fail. \exp(i \pi) = -1.

  45. Matt says:

    limit of the sum 1/2^n is not 1, it’s 2.
    n does include 0, 2^0=1, 1/1=1… 1/(2^1)=1/2
    1+1/2=1.5
    etc.

    so it’ll equals 2, the limit of that sum. and 0.002+e^(2pi)=535,4936…..
    so total 537,49 is what the bill is worth ;)

    graz.

  46. Jarich says:

    It seems to be 2.002, then :)

  47. Jon says:

    Most of the people in here are just failing.
    The sum of the limit is not from 0-infinity. It starts at 1 so it does equal 1. It is an “i” and not a 2, just look at all of the enlarged pictures of it people have posted links to. The description failed and he is actaully paying .002 cents. There have been videos about Verizon and their failures at knowing the cost of messages with their company, so everything in here makes perfect sense.

  48. Jarich says:

    Correction, 1.002

    Please note that no limit is asked, if that was the case, it would be something along the lines of n–>infinity 1/2^n

    So, 0.002-1+2=1.002 :)

    • Mika says:

      Matt’s math is correct if the initial value of n is 0, but n=1 is written.
      Limit of the sum of 1/2^n, where n starts at 1 and goes to infinity is 1.

      Thus we have,
      0.002 – 1 + 1 = 0.002

  49. Marschin says:

    isn’t that e^i(pi) instead of e^2(pi)? e^i(pi) = -1 so the last two terms would cross each other off!

  50. rokmartian says:

    *punching into a calculator*
    So, what number do I divide that by so it spells BOOBLESS on my calculator?

  51. Avis says:

    I’ll just trust that all of you math nerds have this one covered.

  52. PhoenixM says:

    What I can’t help but wonder is: is it really Randall Munroe who posted this here in FailBlog, or is it somebody else posting it but using Randall’s name?

    • ozymandias says:

      It was not Randall, as I assume he would not have included the caption with the bad math, and woul dhave pointed out it was for $.002.

      • PhoenixM says:

        My fail; having seen so many pictures of this check during the two years that it has been floating around the intertubes, I didn’t even bother to read the math-fail caption somebody had put underneath it before posting it to FailBlog.

  53. Bix Nood says:

    Who writes a check these days?

    Honestly.

    • gangbox says:

      I do!

      I don’t do that electronic bill payment bullshit – NOBODY gets to go into my checking account but me and the bank!

      Paper checks RULE!

  54. Tazzy says:

    I love smart people. :)

  55. WankWhisperer says:

    Holy hell there are a lot of stupid f’in people posting… this is also really old. Any body notice the “2006″ on the check? Comments FAIL. (Except this full of WIN comment).

    \-|–

  56. Vulcanasm says:

    MATH FAIL: e^(pi*i) = -1. That check is written for .002 cents.

    • Princess Artemis says:

      Except that he wrote it for $0.002, which is not .002¢…which is what the whole ruckus was about anyway, the difference between the fraction of a dollar and the fraction of a cent.

  57. j says:

    jesus tapdancing christ failblog fail
    it adds up to .002
    like the verizon joke? .002¢ = $.002? get it?
    somewhere in the world, randal munroe makes a facepalm

  58. Vandesdelca32 says:

    That’s a pretty sweet win there…

    I doubt that I would have figured it out.

  59. Jess says:

    lol @ all the math nerds debating what it really says. The fail here is that in attempt to be super witty and clever, this guy has made out a completely invalid check. Do we need to have a course on how to properly fill out a check or something?

    The amount is supposed to be written in words on the line, and numbers in the box.

  60. Skippy says:

    Would that cheque be valid?

    • James says:

      I dunno, but I once sent my credit card company a check for “negative one dollars exactly”, because I had a $1 credit, and they cashed it for $1 (positive). Bastages.

  61. lawlman says:

    VEGETA WHAT DOES THE SCOUTER SAY ABOUT THE CHECKS POWER LEVEL??????????……………………….

    IT’S OVER 9000!!!!!!!!!!!!!!!!22!!!!!!!!!!!!!!!!!!!!11!!!!!!!!!!!!!!!!!!!!2222222222!!!!!!!!!!!!!111111111!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

    9000?!?!?!?!?!?!?!?! WHAT, IT CAN’T BE!!!!!!!!!

  62. bobbintb says:

    that man is my hero.

  63. Bananaclasic says:

    The math after 0.002 is Euler’s Identity. It, in a simplified state, says 0.002+1-1 .
    Or simply 0.002
    The recording of his call to verizon was hilarious.

  64. Ceelala says:

    So everyone STILL adding their opinion on the maths problem……… do you really think anyone actually cares?
    We all get the sentiment without actually caring enough whether or not it actually technically works.

  65. Aja says:

    This is what you get when nerds try to be funny.

  66. Zippish says:

    actually the pic is bull , as you can see , the sum of money written ON the check is e^(i*pi) , i being a complex number , the sum of e^(i*pi) is -1 , so basically he wrote a check for 0.002 and not 500 ~ dollars as written in the description below

    FAIL DESCRIPTION IS FAIL

  67. Zippish says:

    http://xkcd.com/verizon/ for a larger pic so you can clearly see its e^(i*pi)

  68. I always preferred Geography

  69. Linda says:

    goddamn it, the caption on this is one of the biggest fails on this blog. way to take the oldest thing on the internet, misread it, misinterpret it, and completely miss the point of why it’s funny in the first place.
    it says e^iπ, which is -1
    so it’s .002 + -1 + 1 = .002
    it’s a check for .2 cents, i don’t think anyone would write a funny check for a $500+ bill. it’s a response to the epic Verizon math fail where the people don’t know the difference between .002 dollars and .002 cents.
    http://xkcd.com/verizon/

  70. a says:

    Idiots, there’s no limit. That’s a sequence that converges to 1.

  71. Bob says:

    ZOMG! RANDALL!

    *big fan*

    This check is epic win…

  72. Tomical says:

    Randal Munroe GET OUT OF MY HEAD!

  73. Sigh says:

    No surprise someone trying to show off their math skills misinterpreted this all wrong.

  74. mk says:

    is this a failblog fail ?

  75. Raemid says:

    I was asked during a job interview to solve e^(i*pi). I failed, didn’t get the job. Next time I’ll find another way to fail.

    That company failed and fired everyone 1 year later anyway – fails all around.

  76. Andy John says:

    I don’t know if anyone else picked this up, but in the description at the bottom, they said limit, not sum. The limit of that (1/ 2^n) is most certainly 0.

  77. Orange says:

    Does anyone not know that 1/infinity equals zero?

  78. Avlee says:

    I think this man is my new hero.

  79. Math fail by failblog:

    e^2(i*pi) = -1!!

    you don’t believe me, right? so, believe google:

    http://www.google.com.mx/search?q=e^(i*pi)

  80. drexel says:

    Pretty sure that Riemann sum =’s 0 not 1.

    1/infinity =/= 1

    1/infinity => 0

    • orion says:

      bloody idiots. yes, the last term of the SUM is zero but the sum itself is 1. Just sum the first few terms if you don’t believe.

  81. Mike says:

    As an attorney I find this so f*cking funny as it’s likely a totally proper and a legal way to tender payment yet flip Verizon the bird at the same time. Love it. Love it. Love it. Way to be Randal…way to be…

  82. jess1123 says:

    ok… this is for $.002! change the caption! eulers identity =1 – 1 so .002…. get it straight!

  83. john doe says:

    as n approaches infinity, the fraction becomes 1/(infinity) which is equal to zero, right? so it’s actually .002-1+0 which equals -.998. Or I’m way off.

    • orion says:

      bloody idiots. yes, the last term of the SUM is zero but the sum itself is 1. Just sum the first few terms if you don’t believe.

  84. whittytitty says:

    more like check writing fail. what a loser.

  85. failers anonymous says:

    Welcome aboard the Failtrain everyone commenting here. But a special welcome aboard to the writer of the check. The limit as n goes to infinity of 1/2^n is 0 not 1. I’m damn surprised everyone was so savvy about Euler’s Identity and yet you all missed that little glitch. For shame. And before you try to argue that it is 1 and not zero ask your self this, what is 1/infinity ? It is zero fools. Therefore this check is actually for negative .998 dollars. Which brings us to an even greater win, he is paying a negative balance meaning he is writing a check asking Verizon to pay him.

    • PhoenixM says:

      And a fail to you too, for not understanding that the writer of the check is NOT the writer of the failed math explanation beneath the check; the check itself is clever, while the anonymous author of the text underneath the picture of the text is ignorant.

      Incidentally, nowhere on the check is one asked to take a limit. You have a 0.002, you have an instance of Euler’s Identity, and you have a sum of a converging series.

  86. failers anonymous says:

    Damn sum not limit riiiiiiiighhhhtt

  87. failers anonymous says:

    My b

  88. Jim says:

    The real (not imaginary) Fail here is that his check cost more than the $0.002 for which it was made out…

  89. Sidhe Cat says:

    *sigh*
    Thank you, witty regulars, for making all that scrolling^^^ past the MATH WARS^^^ worth at least a chuckle or .002!

  90. bryan says:

    That sum adds up to 2 tards. Its a geometric series pshhhh

  91. Another true story, since I know you guys love my stories.

    I’ve got a friend who lives in Topanga Canyon and he got a gas bill for $0.00. (SoCal Gas). He figured he was OK. A couple weeks later he got another bill for $0.00, but didn’t answer it because it was telling him that he owed nothing.

    A couple weeks after that he got a red shut-off notice because he hadn’t paid his bill for $0.00. I’m not making this up – my imagination isn’t this good.

    So, anyway, he sent them a check for $0.00 A couple weeks later his statement reflected his payment of $0.00 and the threat of shut-off was lifted. Yes, they did put it through the bank. Cancelled check for $0.00.

  92. A little part of me died.

  93. Troll says:

    This thing is retarded. whoever did the math can’t read.

  94. Your Mom says:

    Oh my. I just listened to the recording of this guy on the phone with the verizon folks (on xckd)… these people are stupid. I got what he was getting at in seconds.

    He should have just told the folks he was talking to, to multipy the .002 (the rate per cent) by 0.01 (one cent… duh). That’s where he was stupid. his little examples were just confusing the dumb bints more. He’s also kinda stupid to think he was going to get charged $0.00002 for KB usage when he was ROAMING. regardless of whether or not he knew the rate in the states… you gotta be pretty dumb to think you can use the web that much on your phone while you’re out of the country!! Especially on the Verizon network (which sux and is too expensive! :-D ) *steps off soapbox*

  95. Potato says:

    Lol @ “Pie”

  96. Bobzor says:

    This is really a fail of failblog math skill

  97. K says:

    The Fail in this case is the caption text below.

  98. Bob says:

    Yea, the caption below is fail.

    And in case anyone doesn’t understand 1/2^n, here it is:

    it starts off as 1/2^1, then goes to 1/2^2 to 1/2^3, etc.

    That weird e-shape thing (blanking on the name) says the sum of everything in front of it, which in this case means to have n constantly increasing.

    Now, if you add 1/2 to 0, you are 1 half away from 1. If you add 1/4 to that, you are 1/4th away from 1, and so on. So you always add half of what you need to get there. However, once n reaches infinity, 1/infinity=0, which means you’re at 1.

    So this check is for .002 (lol no labling win!).

  99. None says:

    e ^ (2 * pie) would be quite a lot of cake. Maybe Verizon haz a birzeday?

  100. elew says:

    It would have been a win if Verizon had posted the check.

  101. ReM says:

    No amount of “positive teacher talk” could ever inspire me to learn calculus, but this has.

  102. Ken says:

    you can clearly see it’s i*(pi) on the site of the guy who wrote the
    check http://xkcd.com/verizon/

  103. Tiernan says:

    This would be a failblog fail guys. what you’re saying is e^(2*pi) is actually e^(i*pi) which is -1. Sum from 1 to Infinity of 1/2^n is 1 so the actual amount of the check is .002. Failblog epic fail.

  104. Alan says:

    The cheque amounts to $0.02, the blown up version CLEARLY shows that its Euler’s identity, exp(i*pi) in the middle.

    The joke wouldn’t be as funny if it was for over $500 anyway.

  105. Lolzy says:

    haha i work for bb&t :)

    this is probably one of the better things one would have to deal with

  106. Showdonn says:

    I wonder if you could write something like: “eight cubed minus three squared,” then in the box put “8*3-3*2.” Would it be valid then?

  107. lulz says:

    THIS PICTURE’S MATH IS COMPLETE FAIL.

    e^(ixpi) = -1 this is Euler’s identity
    sum (1/2)^n = 1

    the check is for less than a penny.
    the person who made the text in this picture is a retard.

  108. mh says:

    Euler would be upset his formula was used on a check!

  109. Laney says:

    pi spelling fail

  110. TurboSquid says:

    Unfortunately a grievous mistake has been made here. John Candy was never in the Blues Brothers movies, Jake was played by John Belushi and not John Candy.

    This movie was brilliant and I would hate to see John Belushi’s credit be stolen like this.

  111. AsaZ says:

    Excellent work Mr. Munroe… Enjoyed the memo also, very curious as to whether they actually accepted this payment and whether the bank cleared it…

  112. MrDahut says:

    Nice played.
    I live in NY and our local power authority LIPA are, well to put it simply inept corrupt and always bad at math (in their favor).
    A local Man became a Hero when he wrote all of his checking INFo on a NEW CLEAN pair of tighty whitie’s and mailed it in. LIPA refused to accept payment but the gentlemen persisted. This series of transactions ended up in county and then state court. Final verdict So long as all information is properly formatted and the material present no health hazard it is considerd a viable check. I some how suspect that the case of this check would meet opposition in court only becuase of its written format.
    That being said brilliant

  113. Normal Person says:

    Don’t you guys have a Star Trek convention or something to go to?

  114. CarnivalKing says:

    Here’s the real Fail:

    That’s sigma notation. It is not a limit. It means {(1/1^2) + (1/2^2) + (1/3^2) +…+ (1/infinity^2}.

    That check says .002 + e^(2pi) + Infinity

    Congrats, you gave an infinite amount of money to Verizon. I hope you didn’t actually give them that check or you’re going to be in debt for a very long time.

    • My required name says:

      OMG already! Didn’t you read ANY of the comments? It’s between the “X” and the “R”!!!!!

    • Drew the Jew says:

      Wrong.

      Completely wrong.

      It is an infinite sum, true. But it has a finite value. It’s learned in Calc 1/2 and is not up for debate. If you really want a rigorous proof take a Real Analysis class.

      This was done by the guy who writes XKCD, who was a Phsyics grad from my college.

      • orion says:

        True. And everybody can fu* compute the sum in ten seconds to 4 decimal places… so this just confirms that there’s no hope for humans.

        Someone being complete retard at math: acceptable
        Someone thinking that knowing what apple pie is qualifies them to go correcting randall’s work: humanity fail

      • techphets says:

        The problem is that people are reading the description and not asking themselves “is that really a two?”

        Those who studied only math do the math.

        Those who have actually applied such math realize that something doesn’t make sense here. Recognizing that things do make sense (and even become funny) when something very close to Euler’s identity is replaced with Euler’s identity then tends to cause those minds to say “doh, someone mistook i for a 2, silly person.”

        Or you could just link to the enlarged picture.

        I can see someone writing e^i2pi for some redundant reason but does anyone see a reason to use e^2pi alone?

  115. Math Nerd says:

    no one have notice the problem with limit..
    when u take the 1/2^n to infinity, the answer should be 0 instead of 1..

    • techphets says:

      sigma[1..n] 1/2n = 1

      You can demonstrate this easily:

      1/2^1 = 0.5
      1/2^2 = 0.25
      1/2^3 = 0.125
      1/2^4 = 0.0625
      1/2^5 = 0.03125
      1/2^6 = 0.015625
      1/2^7 = 0.007813

      0.5 + 0.25 + 0.125 + 0.0625 + 0.03125 + 0.015625 + 0.007813 = 0.992188

      If you’re still not convinced, you have only inf – 7 terms to go.

      A formula for the cents would have been good too. If data charges were for 43,200 minutes: regular billing + (43,200 * 0.002) / 100 dollars.

      Too bad nobody tried to force them to honor their contract.

    • PhoenixM says:

      Clearly you aren’t a Math Nerd. It isn’t a limit; it’s a summation.

    • Drew the Jew says:

      As said below its a sum. And you are right if you look at the limit of the terms of the series of the sequence it is infarct convergent to 0. That doesn’t mean any sequence that converges will also converge as an infinite sum. Take sum(1/n) for n 1 to inf. Divergent sum, but a convergent sequence.

  116. mrs_z says:

    Oh, yeah? Well, what’s purple and commutes?

  117. pimanrules says:

    :) XKCD.

    And yes, the math below is wrong. I’m in 8th grade and I knew that….. LOL. It’s equal to .002.

  118. pimanrules says:

    Oh! To the people who say it’s 2(pi):

    http://xkcd.com/verizon/ The original.

  119. Devin says:

    Actually, he didn’t include the “lim” notation in front of the sigma. So really that doesn’t work out.

  120. Vicky says:

    Epic Epic WIN!!!!

  121. A says:

    Actually, this check isn’t even legal. A negotiable instrument must be made for a specific amount.

  122. KarmaJolt says:

    Nice work, except that he wrote (2pie) instead of (2pi).

  123. FAILED says:

    if the n is wrote a bit larger and become 2n instead of 2^n

    he will be broke as it is infinity

  124. Jade says:

    Nice dude!

  125. Gaxe says:

    You guys do realize that the sum is worth 2 and not 1, right ? :)

  126. FAILBLOGFAIL says:

    That’s and ‘i’ not a ’2′… Reading fail.

  127. Mr. Big says:

    He misspelled Pi.

  128. Matt says:

    This is amazing

  129. Annotation/image manipulation FAIL.

  130. carrie says:

    Am I the only person who noticed that the “explanation” at the bottom reads “pie” and not “pi”? Clearly, the comments were written by somebody who didn’t actually know anything about math. And who also couldn’t read a check, because they confused i with 2.

  131. and says:

    caption FAIL… the greek letter is spelled “pi” and it was e to the pi*i which is -1, not e to the 2*pi. So the check is actually worth .002 – 1 + 1 which is .002.

  132. Ticky says:

    I’m sure it’s been pointed out before, but that picture was featured in my university’s engineering student magazine and it’s really bugging me that engineers didn’t even catch it. The cheque clearly says e^i(pi), which is equal to one. So the cheque is worth $.002, which is what makes it funny. So, the cheque is a win, not the faulty math beneath it. I mean, seriously, would it be funny if he was paying over $500? For me, not really.

  133. Marcel says:

    haha “computation fail”!

  134. Mia says:

    Actually, it reads e to the quantity pi times /i/, which is equal to -1. So the amount is actually only $.002.

  135. El Cid Campeador says:

    Its wrong !! The limit summation of 1/ 2^n is not 1. If u divide 1 by an infinitely increasing number , you will get closer and closer to zero. therefore the limit is zero !!

  136. Alan says:

    The summation is 1. How can you add positive numbers and still get a sum of zero?

    I wonder if the cheque would be valid if the guy wrote it in words in the part where he supposed to write it in letters. Like zero point zero zero two plus the exponential of i times pi plus etc etc.

  137. hilsydilsy says:

    Nerd alert.

  138. susiebaby says:

    will you people do my homework?

  139. NO TO REGROUPING says:

    Now, they cash the cheque – after they get someone to decipher it

  140. jgjake2 says:

    ok, let me settle this little 2*pi vs. i*pi argument…Have any of you thought of looking up the original picture and seeing for yourself?

    It’s an i

    if you don’t believe me then go to google and look it up

  141. Josh says:

    It’s not e^2*pi it’s e^i*pi. You can see how the writer makes his 2′s elsewhere on the check. e^i*pi = -1, which cancels out the infinite sum equaling 1 thus making it funny, except for that the end result is 2 tenths of one cent rather than 2 cents, which would be funnier.

  142. NxOhMissFriedxD says:

    i dont care if its right or wrong, this is freaking hysterical!

  143. Robert D Johnson says:

    This is obvious to anyone who has an engineering degree in math or science. (I have an Mechanical Engineering degree from MIT.) Virtually anytime you see “pi” in the exponent area for “e” then there will also be an “i” in the exponent area too. This is standard terminology for trigonometry and complex notation. Everyone knows e^(i*pi) is -1. This is a simple joke. It would be totally out of character to ever write e^(2*pi), and that would give an irrational result with the decimal digits going to infinity, an “impure” answer that no engineer could live by. This looks like a simple check for 2/10 of a cent to me.

    • Robert D Johnson says:

      Also, as some people are misreading, the expression written is “the sum of 1/2^n as n goes from 1 to infinity”. Yes, each term gets smaller and smaller toward 0 but the sum approaches 1. The summation looks like 1/2 + 1/4 + 1/8 + 1/16 + … = 1. Use Google on his name or this topic to see the check enlarged.

  144. justathought says:

    if i got that i would just be like “No.”

    • Bank Her Empty says:

      I work at a bank and am someone that would be in a position to genuinely make a decision on this check, and through all the mathematical debate and intellectual conviction, this is by far the best response.

  145. benhimers says:

    Ok—the guy who tried to wiki Eulers is a dope

    e^iax= cosax + isinax…in this case cos(pi) +isin(pi)= -1 + i(0)=-1

    so it is just .002

  146. Is that e^(2Pi) or e^(i Pi)?

  147. The-Genius-Sisters says:

    As n approches infinity, it grows closer to zero, not one
    He is scamming them out of a dollar,
    also, in order for it to be ligit, he should have put the limit before it
    =)

    • Ray says:

      He doesn’t need ‘limit’ there; that’s a single infinite sum, not a limit of partial sums. (For simple convergent series like this one, they’re the same, but this is not always true: 1+2+3+4+5+… = -1/12, but the sequence of partial sums has no limit in that case.)

    • Shizukarumi says:

      IS NOT A LIMIT IS A SUM, SUUUUM!!!!!!!!!!!!!!!! FROM 1 TO INFINITY = 1!!!!!!!!!!!!!!!!!!!

  148. hi says:

    EPIC WIN!!!!!!!!!!

  149. Rarissa says:

    This FAILs for the misspelling of “pi” in the explination of the equation.

  150. nine says:

    for all them who say that it is 2*pi . . . look at his other twos . . . they all look the same but nothing like the obvious “i” that is in the picture.

  151. konfused says:

    use guyses r al word ima goin 2 slept now causes use guyses r konsfusing my poor liltet bran (me thot pi was 4 eatin not mafs)…..

    p.s.nerdz uses nose mafs

  152. nicole says:

    you guys actually give a shit about this? FAIL.

  153. J says:

    Explanation Fail: pie instead of pi. Nicely done.

  154. Anonymous says:

    You guys are reading it wrong.

    e^(pi*i) equals negative one. Ask your math professor.

    the sum of 1/(2^n) from n=1 to n=>infinity is one.

    two hundreds of a dollar will round down, as 2/10 of a cent can’t really be collected.

  155. beep says:

    i’d just like to point out that he misspelled “pi” ( he said “2pie”) in the explaination. i think the submitter did a fail, himself. =P

  156. Misone says:

    Does anyone else love how in the explanation they wrote pie instead of pi?

  157. nicolatte says:

    get a life

  158. Dan says:

    Any of you guys (and maybe girls) ever watch The Big Bang Theory on Monday nights? Just curious.

  159. Christian says:

    $536.49 for a Verizon bill?? More like Verizon win.

  160. a noob says:

    heh, I love how he gets semi-technical with the math, and then misspells pi…. just made my day XD

  161. ra says:

    ……….freaking smart people……… :D D

  162. not the moron says:

    I cannot believe that nobody saw this…
    because the thousandth place has been used in the equation, you DO NOT round up to 1 when finding the limit of [1/(2^n)]. When rounded to the thousandth, it equals 0.998. When you add the 0.002, that equals 1. So, the check is made out for $0.00. That is why it was never deposited, and there is nothing printed on the MICR line. DUH.

  163. person says:

    with all these ppl commenting, i turned into a FAIL.

  164. Ola says:

    I think it says
    e^i*Pi
    that is equal to -1

  165. MATHMATICS FAIL says:

    lim(1/2^n) when n is approaching infinity is 0, not 1..

    • Shizukarumi says:

      OMG FOR THE LOVE OF JESUS CHRIST IS A SUM, SUM, SUM, SUM,SUM!!!!! GET IT? IS A SUM FROM 1 TO INFITINY SO IT EQUALS 1!. NO IT IS NOT A LIMIT.

  166. MATHMATICS FAIL says:

    WHen the n is approaching 0, then the limit becomes 1..

  167. SomeOne that looked at it in whole says:

    Actually there is only two plausable outcomes…

    .0002 + (-1) + .5 = -0.4998

    or

    .0002 + (-1) + 2 = 1.0002 (retards answer)

    yes Euler’s ID is part of the equation…
    but what about the sumof (1/2^n) since they stipulated that infinite is equal to it’s self and that n = 1 would make that sumof either (1/2^1) or depending on your retardedness (2^1/1)… Which make -0.4998 the most plausable answer… although this is no real answer as I don’t believe that writer of the cheque knew anything about maths!… Any other answer is mere speculation on the base of e^2pi and/or n=0…

  168. Ricky says:

    Holy crap, I plugged this into my calculator and it gave me 536.493655525, which averages out to $536.49. The bank pretty much pwnd that guy.

  169. armanrules says:

    i would give them money, not math

  170. Another Math Geek says:

    My .2 cents:

    e^(pi*i) = -1 is correct. Put in the form e^(pi*i) + 1 = 0 it is considered the most beautiful equation in mathematics because it relates math’s five most significant constants, so there’s no way the guy did something else. Furthermore, close observation reveals that there is in fact a dot over the i, which would obviously not be the case with a 2. Even-further-more, if the i WERE a 2, it would most likely have the same shape as the other two 2′s (not tutus) in the expression, which it does not. Mathematical knowledge, observation, and human behavior all support the e^(pi*i) explanation.

    Sigma (n=1 to infinity) 1/(2^n) = 1 is also correct.

    .002 + (-1) + 1 = .002

  171. Nick says:

    @ “not the moron”:

    Mathematically, even if you want to round to the nearest thousandth, the sum is equal to one. You can take it that he wrote “1″ instead of “\sum_1^{\infty} \frac{1}{2^n}” ; they are identical. As such, the value of the cheque is for $0.002. I haven’t listened to the phone call, but I assume the cheque was supposed to be for $0.02 and the guy who wrote the cheque made a mistake, and meant to write 0.02.

  172. Stacey says:

    thats hot.

  173. Trek222 says:

    This hurts my head so much. People who are trying to interpret this when they have no understanding of math. E^(i*theta) = cos(theta) + i*sin(theta). with theta = pi that means it is cos(pi) + i*sin(pi) = -1 +0 = -1

    Then some idiot started talking about how the limit of 1/(2^n) approaches 0. While this is true, the expression is not a limit. It is sum that essentially 1 after the first 10 terms.

    The expression therefore becomes .002 + (-1) + 1 = .002

  174. Trek222 says:

    Correction

    It is sum that essentially is 1 after the first 10 terms.

  175. dapoochiman says:

    Nicely played. And the math is correct too haha.
    Holla!
    That just isn’t that difficult mathwise either, I’m a sophomore in highschool and i can do that stuff…

  176. kk09 says:

    for the love of all that is holy, y’all need to get a life and quit worrying about the mathematical errors. it’s just meant to be funny!!

    • Anne says:

      Of course, it is funny on it’s own. However understanding the math, that the check is made out for the amount .002 + -1 +1 = 0.002, references something even funnier. It references a claim made by a Canadian Verizon customer who was quoted a data plan at .002 cents/ KB but was charged $.002 (separated by a factor of 100). Yikes! Imagine multiplying a section of any bill by 100! Good job on the basic math Verizon. And finally, it’s funny that the person who made the label underneath didn’t totally understand what Mr. Munroe had meant either.

  177. fudge says:

    It’s actually e^(2 pi e) which is $26152833.54. So it looks like Verizon won.

  178. yarrrrr says:

    Is anyone even reading these comments anymore?

  179. Shizukarumi says:

    YES.

  180. crazy kitty says:

    what now?

  181. I haz maths says:

    Is its teh cherry pi?

  182. VZW4LIFE says:

    FIRST OF ALL THERE IS ONE OBVIOUS PROBLEM WITH THE CHECK… ITS MADE OUT TO VERIZON COMMUNICATIONS WHICH HAS NOTHING TO DO WITH THE ISSUE OF .002 CENTS OR .002 DOLLARS BECAUSE VERIZON COMMUNICATIONS ONLY PROVIDES LANDLINE AND INTERNET SERVICES..ONLY VERIZON WIRELESS PROVIDES CELLPHONES AND MOBILE BROADBAND ACESS SOOO IF THIS CHECK WAS REALLY GOING TO BE SENT TO ANYONE IT SHOULD BE ADDRESSED TO VERIZON WIRELESS … I WORK FOR VERIZON WIRELESS AND THERE IS NO SUCH” BILLING DEPARTMENT” THERE IS ONLY A CUSTOMER SERVICE DEPT WHICH ACTS AS BILLING, ACCOUNTING, TECH SUPPORT, RETENTION ….ALLTHAT! SO… IF YOUR SAYING SOMEONE XSFRD YOU TO A BILLING DEPT I KNOW THAT LINE OF YOUR STORY TO BE FALSE..NOT POSSIBLE.. AND QUITE AMUSING TO SAY THE LEAST!

  183. Nosfer says:

    e^iπ=-1 according to euler’s identity (it’s an i the imaginary unit and not a 2) and sum of 1/2^n=1 so the total money is 0.002.

  184. Joe's Mamma says:

    And the amount of time it took the loser to work this out is completely non-chargeable to Verizon. What a WIN…

    Not…

    • The Mosh says:

      Actually this probably took him about 30 seconds. Since he only intended to pay them the 0.2 cents, all he had to do was write that and then add two things that cancel, which he did. So yeah, it’s a win.

  185. sun says:

    calculus win!

  186. Psycho-Tic says:

    Now thats how you get back at those annoying dept sharks!
    Then again, bankers are normally good at maths, so this wouldn’t really work… but atleast you had fun!

  187. MC Wrench says:

    i didn’t read all comments, so i don’t know if anyone noticed yet.
    but i have to say, that the sum of 1/2^n is 2, because n can be 0;1;2… so there is 1/2^0+1/2^1+… and thats actually 1+1/2+1/4+… ->2

  188. Jacob says:

    Pi spelling fail…

  189. i wonder if the bank would accept it

  190. BigDaddy says:

    explanation fail

    exp (i*pi)=cos(pi)+i*sin(pi)=-1+0=-1

    536, it seems. Jackass

    ‘She’s hot, yes. But can she solve stochastic differential equations?’

  191. Yarrrg says:

    It’s .002. This picture is as old as the internets, and you can google a sharper picture of the check and it’s e^(i*pi) + (sum n = 1 -> infinity) 1/2^n + .002$, which is -1+1+.002, which is .2 cents. I’m done feeding the trolls for now.

  192. someone says:

    Equation:
    {failblog/Winblog-vrizon communication+the stupidity of bush(which equal to infinity BTW)=Comment……

  193. Toby says:

    I just love this one…

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