u notice its the same person who did the verizon maths fail about a month ago?
looks like he was gettting revenge…
for the record its randall munroe, the guy who writes xkcd comics…
Not to be a math nerd… hold on, that’s not completely true. *meekly* I am a bit of a math nerd. In any case, that appears to be e^(i*pi) which is an imaginary phase factor, or by another interpretation, -1. In any case, the writer didn’t pay very much.
*ducks back under ground to do more physics*
First off, I think that the equatin does say “2*pi”, not “pi*i”, but, to clear things up, “i” is an imaginary number, but can be used in certain equations. The e^(pi*i)=-1 equation works because of de Moivre’s formula: e^(x*i)=cos(x)+i*sin(x). Since sin(pi)=0, the second term is cancelled, leaving cos(pi), which happens to be -1. A more detailed explanation can be found here: http://www.math.utoronto.ca/mathnet/questionCorner/epii.html
question, question. I am not very good in math..however, i would just like to ask: isn’t i (as the imaginary number you’re talking about) the square root of negative one? hihi.. just to clarify. if it is so, then i understand de Moivre’s formula now (well,it’s the first time i encountered this one). thanks for the info, very comprehensive;-)
I mean that clearly makes sense … why would he actually pay a decent amount of money to a company that he is trying to get revenge on and mock? Come on people lets just think logical for a second.
Ok well e is an irrational number approximately equal to 2.71828 and 2 x pi is approximately equal to 6.28 which then gives you 2.71828^(6.28)=535.492 then add .002 and he brings it right to the point where they won’t round up to the next cent which is comical and then for the last dollar he has an integral sum which is actually also the definition for the p test in calculus for infinite areas.
fail of higher order math
it’s not e^2pi, its e^i(pi), which, on the complex plane, is -1. This makes sense with the previous Verizon math fail because he should only be paying 2 cents, not two dollars.
You got it wrong, because pi is multiplied to the irrational unit, i, which
equals the square root of minus 1. this number cannot be calculated in
real values, however the formula e^(i*pi) approximates to -1.
The reason why is: The Maclaurin series for sin(x) is x – (x^3)/3! + (x^5)/5! – (x^7)/7!, and so on.
The Maclaurin series for cos(x) is 1 – (x^2)/2! + (x^4)/4! – (x^6)/6!, and so on.
The Maclaurin series for e^x is simply 1 + x + (x^2)/2! + (x^3)/3!, and so on.
So, if we plug in i*x instead of x, we get e^x = 1 + ix – (x^2)/2! – (i*x^3)/3! + (x^4)/4! + (i*x^5)/5! – (x^6)/6!, and so on. The signs change because, obviously, i^2=-1.
Now, if we separate the real and imaginary terms, we get the following.
e^ix = (1 – (x^2)/2! + (x^4)/4! – (x^6)/6!…) + i*(x – (x^3)/3! + (x^5)/5! – (x^7)/7!…)
By substituting in the MacLaurin Series for sin and cos, we get:
e^ix = cos(x) + i*sin(x).
This is Euler’s Formula.
So, in the case that x = pi, e^(i*pi)= cos(pi) + i*sin(pi), or in other words, e^(i*pi) = -1 + i*0 = -1.
The exponent is i*pi, guys. First, that’s what it says. Second, that’s the only way the joke makes sense. e^(i*pi)=-1 to cancel the +1 from the sum, leaving just .002
For the LOVE . . . Randy Munroe got his degree in PHYSICS, e^(i*pi) is a SIMPLE and OFT-USED equation; there is NO beauty in e^(2*pi) and he would never use it. Knowing the context of the check makes it easy to know that this check was made out for $0.002, or .2 cents.
I can’t BELIEVE all the goombas that think that is e^(2*pi) or that e^(i*pi) doesn’t make any sense, because it does.
Of course, that’s just a matter of opinion.
dammit it’s not a iota. It’s not a two either. It’s an i. It clearly has a dot above it. (Something the greek symbol iota does NOT have! Neither does the symbol ’2′ actualy.)
It’s 2pi. It’s obviously what he intended, since the poster is the one who made out the check, and in the caption below it it clearly mentions .002+e^(2pie), which, although misspelled, definitely clarifies it from the source.
This is pointless… It’s i(pi) because otherwise there is no point. e^i(pi) is -1, so it can make sense alone in this case. Go plug it into your calculator. It also makes the check out to .002, the whole misquoted number that started this
well, yes, but e^(pi*i)=-1. It’s called Euler’s identity and is a specific case of Euler’s formula — an incredibly powerful formula that allows you to do some cool stuff.
But who cases about all that junk. look at what the good folks at google have provided.
mabey not… I have done the math on a scientific TI-84 Plus calculator and it works perfectly. i may not be a math nerd but i know how to use the calculator.
one issue.. im pretty sure he wrote e^(2pi) which would be more correct. i think this guy just had messy handwriting and was trying to write small. haha. Im a math geek at heart and stuff like this cracks me up. so im gonna go ahead and assume that its a 2, not an i. if you look closely, it could really be either one. so this guys either really miswrote a check, or knew his stuff. haha. still awesome either way.
Nah, Randal isn’t the guy who got screwed by Verizon. This is just his way of showing support (and it is made of win). Although the text explaining how much the check is for was never a part of it.
I agree. Totally revenge of the nerds. REALLY HILARIOUS! I could totally see myself doing something like this, be it writing the check or solving it-for fun!
Sorry, “spelt” is not the same word as “spelled”, nor is it an older form of
the word unless you go back a few centuries when all spelling was erratic.
It is the past participle of the verb “to spell”. Same goes for “burnt” and
“burned”. They are used in different contexts of the language by those
who know how.
Back to the maths debate…
you guys…are so entertaining.. You comment on this check and you try to do the math? the point is.. It’s pretty funny..and then you go into spelt and spelled and burnt…wow…i can seriously just stalk you guys all day to find out what else you guys talk about.. Kudos..for entertaining me
Actually spelled and burned are incorrect (depending on what
dictionary you use, newer American English probably have highest
chances of including spelled and burned)
There are MANY irregular verbs in English that only in the last 15 years
or so has the ‘regularized’ spellng been accepted anywhere…
well … the comment below is mathematically correct, so no fail in that … it’s only the fact that he saw the i Pi as 2 Pi – so no math fail here … only transcription fail
Have we learned anything from this experience? Perhaps something along the lines of not slamming someone’s reading comprehension without making sure you have the right of it? All rightee then!
Not to be a nitpicker, but the root of -1 is not i. this is a common misconception. I can’t be bothered to look up the exact proof (it would be on wikipedia), but you get all kinds of weird things if you assume i = sqrt(-1).
What is, however, correct, is that i^2 = -1.
What makes this work, but not the other way around, is that we’re dealing with the imaginary plane here. both i^2 and (-i)^2 = -1, just like with real square roots. A function can only have one value for a given parameter, though, so we solve this in real maths by having sqrt(x) only return the positive square root of x. However, in the complex plane there is no such thing as a positive or negative value.
What Roy referred to is the fact that in coming up with the definition of the complex field in terms of existing fields required the definition of an element who when multiplied with itself gave the result -1. Therefore it turns out that i=sqrt(-1) but ONLY as long as the meaning of sqrt(-1) is understood. If you ask what *the* value of sqrt(-1) is you haven’t understood square roots. (-i)^2 = -i*-i = i^2. The problem is that sqrt(-1) is ambiguous (satisfied by both i an d -i) but i^2=-1 is not ambiguous. The other major problem is that dumbass spanners like RC exist. They say other people are full of crap when they have no idea what the person they are accusing is talking about because they are too dumb to realize they are a mental capacity FAIL. twat.
Generally, the square root operation is defined such that sqrt(4) = 2, and sqrt(-1) = i. Such a “mistake” is necessary for sqrt to be considered a function, because at every point there must be a choice between the 2 (or in the case y = 0, 1) solutions to the equation x^2 = y. While it is not correct to say that “i is the number whose square is -1″, it is perfectly valid to say that “i is the square root of -1″.
Whether such a function should be called a “square root” is more or less philosophical, but as a matter of historical fact, it is. Therefore, as a matter of historical fact, the common interpretation of the statement “i is the square root of -1″ is mathematically valid.
Wrong. The square root of a number is ONLY the positive number that when squared yields the original number. This is a very common mathematical convention. Think about it, if you let a function f(x)=sqrt(x) and the square root yields BOTH a positive and a negative number, you now have a function with two dependent values for each independent value at all but one point, which does not meet the definition of function.
This is why we express things as sqrt(x) or -sqrt(x). If what you were saying were true, they’d be interchangeable. You can even see this in simple mathematics such as the quadratic formula.
Also, it’s e^i(pi). The thing goes back to Verizon Math when they repeatedly told the guy that the roaming rate in Canada was .002 cents per kilobyte, but instead charged him .002 dollars per kilobyte and like four different reps didn’t realize that there was a DIFFERENCE between the two, and refused to do anything to correct the situation.
The check wasn’t written by the original guy, but Randall Munroe, a comedian, after all was said and done.
Every complex number (that includes all real numbers like 2, and all purely imaginary numbers, like i) has two square roots.
And three cube roots.
And n n-th roots.
The common √ symbol (assuming it shows up correctly) does indeed refer t he principal root (i.e. the root that has the same sign as the number of which it is a root) and doesn’t apply to i.
Duh was half-right. i is ONE OF the SQUARE roots of -1. The other square root of -1 is -i.
FOR EVERYONE SAYING IT’S i*PI, IT IS 2PI, HE’S WRITING OUT HIS ACTUAL BILL AMOUNT, JUST IN ADVANCED MATHEMATICS THAT THE AVERAGE ACCOUNTANT FOR VERIZON WOULD PHAIL AT. READ THE CAPTION BELOW THE CHECK THAT IS STILL PART OF THE PICTURE. IT SAYS EXACTLY WHAT HE INTENDED.
I like how everyone is debating the e part of it, when the caption says 1/2^n as n approaches infinity is = 1 when its equal to zero. as n reaches infinity, the denominator gets gigantic, which makes the fraction negligible.
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.)
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.
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 ^^
The guy got his full refund 3 a little over 2 years ago. There is actualy a 22 minuit more painfull version you can find on the web where he talks to 5 people who still dont understand the math and eventualy offer him a %50 credit.
I imagine she told everyone she knows and was laughing about it with her coworkers all day. Her extended family is probably sick of hearing about it by now.
“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.
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.
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$.
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 …
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:
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!
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.
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.
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.
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.
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
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.
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?
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.
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).
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.
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
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.
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.
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.
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.
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
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/
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.
I was just thinking that, actually – “How could 1 over an infinitely large number be anything but an infinitesimally small number? Oh yeah, ‘cuz people are dumb.”
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…
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.
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.
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.
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.
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! ) *steps off soapbox*
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.
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.
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.
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
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.
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.
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
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?
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.
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.
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.
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.
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 !!
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.
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.
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.
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.
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.
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
=)
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.)
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.
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.
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…
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.
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.
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.
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…
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 $.002 (separated by a factor of 100). Yikes! Imagine multiplying a section of any bill by 100! Good job on the basic math Verizon. And finally, it’s funny that the person who made the label underneath didn’t totally understand what Mr. Munroe had meant either.
FIRST OF ALL THERE IS ONE OBVIOUS PROBLEM WITH THE CHECK… ITS MADE OUT TO VERIZON COMMUNICATIONS WHICH HAS NOTHING TO DO WITH THE ISSUE OF .002 CENTS OR .002 DOLLARS BECAUSE VERIZON COMMUNICATIONS ONLY PROVIDES LANDLINE AND INTERNET SERVICES..ONLY VERIZON WIRELESS PROVIDES CELLPHONES AND MOBILE BROADBAND ACESS SOOO IF THIS CHECK WAS REALLY GOING TO BE SENT TO ANYONE IT SHOULD BE ADDRESSED TO VERIZON WIRELESS … I WORK FOR VERIZON WIRELESS AND THERE IS NO SUCH” BILLING DEPARTMENT” THERE IS ONLY A CUSTOMER SERVICE DEPT WHICH ACTS AS BILLING, ACCOUNTING, TECH SUPPORT, RETENTION ….ALLTHAT! SO… IF YOUR SAYING SOMEONE XSFRD YOU TO A BILLING DEPT I KNOW THAT LINE OF YOUR STORY TO BE FALSE..NOT POSSIBLE.. AND QUITE AMUSING TO SAY THE LEAST!
Actually this probably took him about 30 seconds. Since he only intended to pay them the 0.2 cents, all he had to do was write that and then add two things that cancel, which he did. So yeah, it’s a win.
Now thats how you get back at those annoying dept sharks!
Then again, bankers are normally good at maths, so this wouldn’t really work… but atleast you had fun!
i didn’t read all comments, so i don’t know if anyone noticed yet.
but i have to say, that the sum of 1/2^n is 2, because n can be 0;1;2… so there is 1/2^0+1/2^1+… and thats actually 1+1/2+1/4+… ->2
It’s .002. This picture is as old as the internets, and you can google a sharper picture of the check and it’s e^(i*pi) + (sum n = 1 -> infinity) 1/2^n + .002$, which is -1+1+.002, which is .2 cents. I’m done feeding the trolls for now.
Thanks for another excellent post. The place else may just anybody get that kind of info in such an ideal method of writing? I’ve a presentation next week, and I am at the look for such info.
Just want to say your article is as astonishing. The clearness for your post is simply nice and i could suppose you’re an expert on this subject. Fine with your permission let me to clutch your RSS feed to stay updated with impending post. Thank you one million and please keep up the rewarding work.
Good luck with that one!
u notice its the same person who did the verizon maths fail about a month ago?
looks like he was gettting revenge…
for the record its randall munroe, the guy who writes xkcd comics…
u r such a stalker
And you are Randall Munroe??
Gotcha!
Not to be a math nerd… hold on, that’s not completely true. *meekly* I am a bit of a math nerd. In any case, that appears to be e^(i*pi) which is an imaginary phase factor, or by another interpretation, -1. In any case, the writer didn’t pay very much.
*ducks back under ground to do more physics*
thus, he is paying 0.002 (is he paying 0.002 Dollars ? )
Must be a hell of a talker.
It is, of course, a matter of opinion.
It’s not a matter of opinion – a larger version shows it is indeed
e^i(pi))
http://themostboringblogintheworld.files.wordpress.com/2006/12/verizon.jpg
So yeah, 0.002 -1+1 = $0.002
There’s a whole article on it as he was quoted an incorrect price.
that too, is a matter of opinion
My opinion of your opinion is is a matter of fact.
Which is, of course, simply my opinion.
Opinion Win!
Fail! i^1 = i. Anyways, its a 2.
This is clearly visible on larger images on other sites.
It is clearly 0.002 + e^(i * pi) + sum (1/2^n).
This does clearly add up to $0.002.
Clearly.
but i is imaginary.
I isn’t! Unless we’s speaking of ideal forms, then maybe I is…..
First off, I think that the equatin does say “2*pi”, not “pi*i”, but, to clear things up, “i” is an imaginary number, but can be used in certain equations. The e^(pi*i)=-1 equation works because of de Moivre’s formula: e^(x*i)=cos(x)+i*sin(x). Since sin(pi)=0, the second term is cancelled, leaving cos(pi), which happens to be -1. A more detailed explanation can be found here: http://www.math.utoronto.ca/mathnet/questionCorner/epii.html
it says i(pi)
It’s a nice try, but it’s not DeMoivre’s formula. It’s Euler’s formula with an argument of pi.
question, question. I am not very good in math..however, i would just like to ask: isn’t i (as the imaginary number you’re talking about) the square root of negative one? hihi.. just to clarify. if it is so, then i understand de Moivre’s formula now (well,it’s the first time i encountered this one). thanks for the info, very comprehensive;-)
I mean that clearly makes sense … why would he actually pay a decent amount of money to a company that he is trying to get revenge on and mock? Come on people lets just think logical for a second.
That’s no plus sign.
I’m clearly unclear that your statement is within reasonable clarity. Just to be clear, in case you’re unclear.
Oh dear.
i don’t think he got it.
he obviously never saw the video
you guys do know that the bank has to process this right? not verizon
prolly never listened to the audio then. she is so stupid it hurts.
i shure dont XD
Amnh… no he really don’t get it…
Yes. .002 dollars… he payed Verizon this check and they needed .002 dollars. so he made it uber confusing for them.
xkcd
I think he misplaced his decimal….it would be so much funnier if he sent them his “2 cents”.
they have to round down when cashing the check so he is essentially giving them $0.00
Do you work for Verizon?
Ok well e is an irrational number approximately equal to 2.71828 and 2 x pi is approximately equal to 6.28 which then gives you 2.71828^(6.28)=535.492 then add .002 and he brings it right to the point where they won’t round up to the next cent which is comical and then for the last dollar he has an integral sum which is actually also the definition for the p test in calculus for infinite areas.
Which is fine since Verizon is – at least at times – irrational as well. I have stories.
Let’s just all agree that Verizon blows, and this guy pwn’d them.
fail of higher order math
it’s not e^2pi, its e^i(pi), which, on the complex plane, is -1. This makes sense with the previous Verizon math fail because he should only be paying 2 cents, not two dollars.
actually, it’s 2 tenths of a cent… funny, I wanted to comment
about the i pi but when I read this, I think this stuff is settled…
that’s not funny.
An Imaginary clue? Isn’t the square root of a negative imaginary?
ACTUALLY…..its two one-hundredths of a cent….notice how there are 2 zeros in front of it.
ML
yea i make a mistake…0.002 its 2 one-thousandths of a cent.
BUT….$0.002 (2 10ths of a cent) is correct.
ML
actually, it is 2 tenths of a cent: the u.s. monetary system uses base 100 (100 cents=11 dollar) so it is 2 tenths
oh and it doesnt make sense to say 2 one-thousandths, its 2 thousandths =)
i meant 1 dollar lol
are you guys nuts? i = square root of -1, not -1. Also, someone said it’s an integral sum? NO IT IS NOT, it is an infinite series….
You got it wrong, because pi is multiplied to the irrational unit, i, which
equals the square root of minus 1. this number cannot be calculated in
real values, however the formula e^(i*pi) approximates to -1.
it doesn’t approximate to -1.
e^(i*pi) EQUALS -1 EXACTLY.
The reason why is: The Maclaurin series for sin(x) is x – (x^3)/3! + (x^5)/5! – (x^7)/7!, and so on.
The Maclaurin series for cos(x) is 1 – (x^2)/2! + (x^4)/4! – (x^6)/6!, and so on.
The Maclaurin series for e^x is simply 1 + x + (x^2)/2! + (x^3)/3!, and so on.
So, if we plug in i*x instead of x, we get e^x = 1 + ix – (x^2)/2! – (i*x^3)/3! + (x^4)/4! + (i*x^5)/5! – (x^6)/6!, and so on. The signs change because, obviously, i^2=-1.
Now, if we separate the real and imaginary terms, we get the following.
e^ix = (1 – (x^2)/2! + (x^4)/4! – (x^6)/6!…) + i*(x – (x^3)/3! + (x^5)/5! – (x^7)/7!…)
By substituting in the MacLaurin Series for sin and cos, we get:
e^ix = cos(x) + i*sin(x).
This is Euler’s Formula.
So, in the case that x = pi, e^(i*pi)= cos(pi) + i*sin(pi), or in other words, e^(i*pi) = -1 + i*0 = -1.
Shit, you need to get a life, seriously dude.
Nice proof.
p test lol
He could have written whatever he wanted and they wouldn’t know if it was correct or not, they can’t even understand third grade math…watch the video.
That’s e^(2*pi), not i*pi.
The exponent is i*pi, guys. First, that’s what it says. Second, that’s the only way the joke makes sense. e^(i*pi)=-1 to cancel the +1 from the sum, leaving just .002
BigJ’s eyesight – FAIL
Whoever mucked up the picture trying (incorrectly) to explain the joke – DoubleFAIL
For the LOVE . . . Randy Munroe got his degree in PHYSICS, e^(i*pi) is a SIMPLE and OFT-USED equation; there is NO beauty in e^(2*pi) and he would never use it. Knowing the context of the check makes it easy to know that this check was made out for $0.002, or .2 cents.
I can’t BELIEVE all the goombas that think that is e^(2*pi) or that e^(i*pi) doesn’t make any sense, because it does.
Of course, that’s just a matter of opinion.
Beside, look at the way he writes his 2′s. The character in the
exponent looks nothing like the other 2′s.
At a first glance I thought it was e^(i*pi) too, but it’s not. It is e^(2*pi), which works out fine
Nope, it’s definitely e^(i pi). I stand corrected.
lol, its 2*pi, now go take a deep breath
Will you nerds just come to a consensus already so we can enjoy the joke?
It actually is 2*pi, if you look really closely. GO NERDS!!!! W00T!!!
I am sorry but it is actually the symbol iota or the greek I; that is okay I thought it was it was Tau or the greek t
dammit it’s not a iota. It’s not a two either. It’s an i. It clearly has a dot above it. (Something the greek symbol iota does NOT have! Neither does the symbol ’2′ actualy.)
there is a link above that gets a larger picture, look at it and its definately i with a curly tail
yea u tell them
It’s 2pi. It’s obviously what he intended, since the poster is the one who made out the check, and in the caption below it it clearly mentions .002+e^(2pie), which, although misspelled, definitely clarifies it from the source.
its not 2*pi Compare the i (or two if you insist) to his other 2s. They look not REMOTELY similar. it’s i*pi
No, really, it’s e ** i pi, look at the high-resolution version at XKCD.
It’s not ambiguous at all.
that’s also what i thought at first, but look closer: it’s a two
You suck.
big time
it’s e^(2*pi)
i^2 is -1. i by itself is just an imaginary number.
All numbers are imaginary. Only numerals have a physical manifestation.
CAN SOME1 PLZ EXPLAIN TO ME HOW 2 PAY VERIZON WITH IMAGINARY MONEY!??
This is pointless… It’s i(pi) because otherwise there is no point. e^i(pi) is -1, so it can make sense alone in this case. Go plug it into your calculator. It also makes the check out to .002, the whole misquoted number that started this
well, yes, but e^(pi*i)=-1. It’s called Euler’s identity and is a specific case of Euler’s formula — an incredibly powerful formula that allows you to do some cool stuff.
But who cases about all that junk. look at what the good folks at google have provided.
http://www.google.com/search?hl=en&safe=off&rlz=1C1GGLS_enUS308US308&q=e^(i*pi)&btnG=Search
i is NOT by itself in the check, it’s with pi in the exponent of e.
That puts it in the form of Euler’s identity:
http://en.wikipedia.org/wiki/Eulers_identity
i’m pretty sure that’s a 2
that’s exactly what i thought too.
mabey not… I have done the math on a scientific TI-84 Plus calculator and it works perfectly. i may not be a math nerd but i know how to use the calculator.
=)
one issue.. im pretty sure he wrote e^(2pi) which would be more correct. i think this guy just had messy handwriting and was trying to write small. haha. Im a math geek at heart and stuff like this cracks me up. so im gonna go ahead and assume that its a 2, not an i. if you look closely, it could really be either one. so this guys either really miswrote a check, or knew his stuff. haha. still awesome either way.
indeed… and on that note, spelling ‘Pi’ fail!
Actually, I think it’s a 2, not an “i”. I thought it was an “i” at first and was puzzled. Now I am not.
That’s exactly what I thought — looks like e^ (i*pi), not e^(2pi). I like our version better. ‘Tis funnier.
GAHHHH!!!
MATH!!!!
Raptor Jesus????? Fuzzy?
it’s not an i, it’s a 2, says so in the caption below the picture.
No, what you’re doing is mistaking 2 for i. He specifically notes that it was e^2pie
Ragidandy : Does physics make your eyes hurt???
Does E=mC^i?
No, because in bigmouthing your supposed knowledge, you mistaked a “2″ for an “i”.
pWned… and you are a LITTLE bit of a math nerd, indeed…
i isnt -1 its the square root of -1 so in other words i squared equals -1
that “i” is a two… poorly resolved image throws you off
OMG its raptorjesus!
i’ve missed you brotha!
No – Because it’s not the same person.
The check is a reference to the verizonmath thing, though.
…aaaand fail
Nah, Randal isn’t the guy who got screwed by Verizon. This is just his way of showing support (and it is made of win). Although the text explaining how much the check is for was never a part of it.
http://xkcd.com/verizon/
LOL That’s pretty good. Revenge of the nerds!
Don’t mess with nerds lest they mess with the LHC.
Meh. They already tried to kill us with that thing. Turns out, they didn’t.
No, silly nerds… Why are you swimming on your back?
I agree. Totally revenge of the nerds. REALLY HILARIOUS! I could totally see myself doing something like this, be it writing the check or solving it-for fun!
“the guy” who got screwed by Verizon? There was just one?
Yep. He worked for NASA for a while and this is quite appropriate.
It’s no surprise it’s Randall…
xkcd comics eh… cool. thats neat to know
MATH FAIL
e^(i pi) as in http://en.wikipedia.org/wiki/Euler%27s_identity
0.002 + (-1) + 1
Verizon just billed somebody for $0.002
Exactly… Someone tried to use higher math but truly failed.
and they spelt pi wrong
spelt?!! really?!
spelt is an older alternative to spelled. it is completely acceptable to use.
Yeah, write. Spellling is my fortay two.
And it is also a grain.
And spelled splet wrong.
Spelt is a perfectly acceptable alternative spelling of spelled, much like burnt and burned.
Also, a species of wheat.
This is true.
The above statement is a lie.
(What now?!?)
Nothing.
The above sentence is false.
(What now?!?)
What indeed?
It’s a matter of opinion. Or a meter of old pinion.
It’s a perfectly cromulent word.
I thought burnt was the participle and burned was the verb… are they interchangable?
Sorry, “spelt” is not the same word as “spelled”, nor is it an older form of
the word unless you go back a few centuries when all spelling was erratic.
It is the past participle of the verb “to spell”. Same goes for “burnt” and
“burned”. They are used in different contexts of the language by those
who know how.
Back to the maths debate…
A certain dragon might disagree with you.
you guys…are so entertaining.. You comment on this check and you try to do the math? the point is.. It’s pretty funny..and then you go into spelt and spelled and burnt…wow…i can seriously just stalk you guys all day to find out what else you guys talk about.. Kudos..for entertaining me
Actually spelled and burned are incorrect (depending on what
dictionary you use, newer American English probably have highest
chances of including spelled and burned)
There are MANY irregular verbs in English that only in the last 15 years
or so has the ‘regularized’ spellng been accepted anywhere…
dove vs dived
burnt and burned are different in usage.
Ex: The barbeque was burnt.
The barbeque burned.
Burnt = adjective
burned = preterite tense of burn, verb
well … the comment below is mathematically correct, so no fail in that … it’s only the fact that he saw the i Pi as 2 Pi – so no math fail here … only transcription fail
a small correction: the comment below the picture
indeed! and depending on how many terms of n you go to, it’ll come you 0.998, so the sum’ll be 0.
It’s quite clearly specified that it’s a series (from 1 to Infinity) which is 1 … so no place for creativity there, sorry :p
Wrong…you fail.
The check isn’t for e^(i*pi)
The check is for e^(2*pi)
lrn2read. the link explains it all. this link was already posted. You FAIL.
the check is for e^(i Pi) =)
larger picture: http://xkcd.com/verizon/verizon.jpg
now i really don’t know how you can see a 2 here??
Have we learned anything from this experience? Perhaps something along the lines of not slamming someone’s reading comprehension without making sure you have the right of it? All rightee then!
This!
i is an imaginary number not a real number
AKA the root of -1 is i….
2 is not i
2 would be viewed as e^n pi
Not to be a nitpicker, but the root of -1 is not i. this is a common misconception. I can’t be bothered to look up the exact proof (it would be on wikipedia), but you get all kinds of weird things if you assume i = sqrt(-1).
What is, however, correct, is that i^2 = -1.
What makes this work, but not the other way around, is that we’re dealing with the imaginary plane here. both i^2 and (-i)^2 = -1, just like with real square roots. A function can only have one value for a given parameter, though, so we solve this in real maths by having sqrt(x) only return the positive square root of x. However, in the complex plane there is no such thing as a positive or negative value.
HTH.
dude you are full of crap
I’m full of carp. Any suggestions?
What Roy referred to is the fact that in coming up with the definition of the complex field in terms of existing fields required the definition of an element who when multiplied with itself gave the result -1. Therefore it turns out that i=sqrt(-1) but ONLY as long as the meaning of sqrt(-1) is understood. If you ask what *the* value of sqrt(-1) is you haven’t understood square roots. (-i)^2 = -i*-i = i^2. The problem is that sqrt(-1) is ambiguous (satisfied by both i an d -i) but i^2=-1 is not ambiguous. The other major problem is that dumbass spanners like RC exist. They say other people are full of crap when they have no idea what the person they are accusing is talking about because they are too dumb to realize they are a mental capacity FAIL. twat.
assume 2 = sqrt(4).
What is, however, correct, is that 2^2 = 4.
What makes this work, but not the other way around, is that we’re dealing with real numbers here. both 2^2 and (-2)^2 = 4,
Does that make any sense to you or to anyone here?
In complex numbers we solve that same problem by forcing the angle to be in [180, -180[
There is no such thing as ‘the’ root of a number. Every number has two (square) roots. We just pick whichever one is convenient.
0?
Is that an actual number, or the absence of numbers?
Math nerds need not attack, I am making a joke (or trying to, at least).
Prequel to Revenge of the Nerds – Attack of the Nerds: Mathematical Annihillation.
0 has two roots, they just happen to be the same number.
Untrue.
Zero has one root.
Generally, the square root operation is defined such that sqrt(4) = 2, and sqrt(-1) = i. Such a “mistake” is necessary for sqrt to be considered a function, because at every point there must be a choice between the 2 (or in the case y = 0, 1) solutions to the equation x^2 = y. While it is not correct to say that “i is the number whose square is -1″, it is perfectly valid to say that “i is the square root of -1″.
Whether such a function should be called a “square root” is more or less philosophical, but as a matter of historical fact, it is. Therefore, as a matter of historical fact, the common interpretation of the statement “i is the square root of -1″ is mathematically valid.
Wrong. The square root of a number is ONLY the positive number that when squared yields the original number. This is a very common mathematical convention. Think about it, if you let a function f(x)=sqrt(x) and the square root yields BOTH a positive and a negative number, you now have a function with two dependent values for each independent value at all but one point, which does not meet the definition of function.
This is why we express things as sqrt(x) or -sqrt(x). If what you were saying were true, they’d be interchangeable. You can even see this in simple mathematics such as the quadratic formula.
Also, it’s e^i(pi). The thing goes back to Verizon Math when they repeatedly told the guy that the roaming rate in Canada was .002 cents per kilobyte, but instead charged him .002 dollars per kilobyte and like four different reps didn’t realize that there was a DIFFERENCE between the two, and refused to do anything to correct the situation.
The check wasn’t written by the original guy, but Randall Munroe, a comedian, after all was said and done.
Every complex number (that includes all real numbers like 2, and all purely imaginary numbers, like i) has two square roots.
And three cube roots.
And n n-th roots.
The common √ symbol (assuming it shows up correctly) does indeed refer t he principal root (i.e. the root that has the same sign as the number of which it is a root) and doesn’t apply to i.
Duh was half-right. i is ONE OF the SQUARE roots of -1. The other square root of -1 is -i.
he’s right
Your lips are moving, but all I hear is blah, blah, blah……
The “what now” is that Verizon “loses” his check and he has to pay late fees.
I would have been more impressed had Verizon cashed the check. They didn’t, there is no transaction data on the bottom right of the check.
Uh…or he scanned it before mailing it…
FOR EVERYONE SAYING IT’S i*PI, IT IS 2PI, HE’S WRITING OUT HIS ACTUAL BILL AMOUNT, JUST IN ADVANCED MATHEMATICS THAT THE AVERAGE ACCOUNTANT FOR VERIZON WOULD PHAIL AT. READ THE CAPTION BELOW THE CHECK THAT IS STILL PART OF THE PICTURE. IT SAYS EXACTLY WHAT HE INTENDED.
Writing something in caps does not make it true.
True that, just makes it annoying to read.
True, in fact someone that annoying is most certainly wrong.
Randall Munroe is my hero
spelling FAIL
What has argueing on the internet and taking part in the Special Olympics got in common?
Even if you win you’re still a retard.
My father in law who has a degree in mathematics had this to say
I’m the kind of geek that checks the math……
Text is hard for this stuff but, The check says it is for [0.002 + e ^(i*pi)] + Sum one to infinity of 1/(2^n)
e^(i*pi) = -1 Euler’s Identity. http://en.wikipedia.org/wiki/Euler%27s_identity
The summation converges to 1.
So our Hero wrote his check for $(0.002 – 1 + 1) = 2 mils.
The cheap bastage.
Dad Geoff
also the limit as n approaches infinity of 1/(2^n) is actually 0, not 1. learn some basic calculus
i also wanted to write that, but luckily i found your comment
wahat i wanted to add:
it says [0.002+e^(2pie)]
they must be either talking about the number “pie” (wtf it’s called “pi”) or about e^(2pi*e), which isn’t written on the bill
also, i is not equal to -1 (i^2 is). i=sqrt(-1)…an imaginary number, get an education people
I like how everyone is debating the e part of it, when the caption says 1/2^n as n approaches infinity is = 1 when its equal to zero. as n reaches infinity, the denominator gets gigantic, which makes the fraction negligible.
Its funny because the people at the accounting dept are going to void this check based on their unwillingness to do math.
Randall Munroe?!?!?! World-famous creator of xkcd.com?!?!?!!?!?!?!?!
that is not e^2*pi. it is e^i*p, i being the square root of minus 1, e^i*pi is -1, so the check is actually for $0.002
You to can hear how bad verizon failed on this on .
recording – http://imgs.xkcd.com/verizon_billing.mp3
i peint all my checks like that ☺
I pay all of my bills with imaginary numbers.
Where do you see “i” in there?
Verily you are a saucy lad.
I’m sure YOU would like some of his “sauce,” eh? *wink wink* say no more
Gross, Huggy. Just… gross.
you’re only saying that cos i kinda revealed my age, if it was still a secret it wouldn’t be gross at all
No no, thats “I” not “i” -facepalm-
It turns me on when you pretend you are.
Let’s be honest – everything turns you on, honey. It’s one of your most endearing qualities.
Everything on you, my dear.
The only thing I want ‘on’ me is you, precious.
On, in, above, over, below, beside or against. It is your choice.
You are so accommodating. I choose “yes.”
ha ha the funny part is loufail is probably terrified of the notion of being near a girl
Wow, I hope not, or I just wasted $1,076 on a plane ticket and a hotel.
You are no girl but a woman. And I am not terrified but trembling.
Trembling already, amor? It’s a long time until 20:30.
20:30 was like 2.5 hours ago…
Long time in the clock, longer in my heart.
You are forever in my heart. Is that long enough for you?
Forever, with you, sounds just right (and for sure that heart of yours is big enough).
OK, I’ve cancelled my appointments for the rest of my life.
My agenda is burnt. I used the fire you started on me.
May I have some more of that “yes” of you? I will tell you was I was asking for afterwards; I hope you like it.
My answer to all of your questions is “yes.”
Mookie..
Like .. everything?
the beginning of a web marriage or cybersex?
I see “i” just before the pi, in the power of “e”, making it a cheque for $0.002
dito
gimme some oxycontin. i have a dito head ache.
I don’t think people will get the Limbaugh reference. It’s nice to see a comment thread with some actual adult trash talk.
Me like pie.
Comment win!
Epic
Verizon wanted it all, but they can’t have it. It’s in their face but they can’t grab it.
I’m losing my Faith. No More do I trust them.
I like to watch fish flop.
It’s ok to hurt fish as they don’t have any feelings.
You have the Dilbert desk calendar! HAHAHA!
Who what where when how?
Shoe shat shere sham wow ?
Poo pat pear pam’s POW!
Sue sat near Sam’s cow?
Sue sat near Sam’s sow?
Is he saying “Pal”?
Don’t you play coy with me!
Boy! Don’t you play with me! (I know you’re female, but girl wouldn’t have worked with your comment. I claim artistic license).
I have no calendar.
*Pops out of nowhere*
That is because Moomins are ever-lasting?
*SQUEEZE*
*Vanishes*
And LARRY is getting LAAAAARGER!
What is it?
“Randall Patrick Munroe you’re my heeero”
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
That is a matter of opinion.
you can clearly see it is an i not a 1/2
I mean a 2, it’s not a 2… i fail
Getting the reference fail.
yeah, sorry, I’m not very cultured
Check failblog for “Verizon math fail”.
you remember your fails way too well, I only remember it vaguely asan arguement about basic maths and his internet bill…
Young brains are easily distracted. Usually by potential sex partners.
that and my penis
That’s what I was talking about.
I think tha was an insult… hang on, no it’s not
Bunch math nerds…
Still a WIN!
yes, I am currently trying to make myself do my maths homework as we speak, obviously my efforts are failing
Homework? Just how old are you?
wouldn’t you like to know?
also, if a^2=-15, HOW DOES a=+-1?!?!?!?!?!?!?!??!?!
that right there- hilarious
Dang that sucks Huggy, according to fier, you are negative hilarious.
Math is not a matter of opinion, Rogger is correct!
Getting the reference fail pt. 2.
Electric Bugaloo.
I’m afraid this will be a multi-part series.
Oh no. Did I start another lame joke like the counting of ‘win’ the other day? My apologies.
Au contraire, mon frère! Your joke was not lame! I was just acknowledging that you could expect further failures to recognize your reference!
*hugs*
*hugs back*
As long as my comment doesn’t provoke 100 “It’s NOT a matter of opinion you moron” replies that’s fine for me.
high-school education wins!
mine’s failing so far…
Win
[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.
e?
*drops*
*Picks* Sorry about that
chemicals, like math, will never bring true happiness
Not even hormones?
hormones work, ever since menopause, hormones work a treat
*scratches testicles* hahahaha
sorry, these hormones make me terribly itchy
Unlike math they can bring lots of fake happiness for a limited time.
Fake works for me! Roll me one of your funny “cigarettes” will ya’, Arthur?
thats not a chemical, and it brings true happiness. puff puff pass?
*rolls a big one*
But for a limited time.
*puff, puff, passes*
Hey, at least it’s not crack
*approves of Arthur Eld’s application*
*puff, puff, passes*
Handwriting fail, on second thought, can’t determine if it is an i or a 2. =P
Clearly, no sane person would even think of something like e ^ ( i * pi )
…except for you maybe =P
and Randal Munroe, the creator of xkcd
Wait, are you calling Randall Munroe sane?
Actually a very sane person did. His name was Euler, the most brilliant mathematician of all time. Nice try though.
[B]argueably[/B] the most brilliant… brilliantess is subjective
HTML fail
use < brackets
argueably
“Brilliantess” is not subjective when it comes to something objective like math, you are either brilliant or you are not.
“Basic rules of the world FAIL”.
Brilliantness is a, like everything, a multidimentional space of micro-quantized factor gradients.
And the brilliantness of a person is an subset/area of that space.
The opposite is called “brillantness” (sic).
I prefer brilliance.
His name was Euler, but his friends called him Loose.
I think I saw him hangin’ out at eighth and forty-deuce.
math fail dude… that’s actually what’s so clever about this check
e^(i*Pi)=cos(Pi)+i*sin(Pi)=-1
0.002-1+1=0.002 dollars for the bill
Just another Failblog’s fail.
it’s not “i”, it’s “2″
No it’s not. Read about the Euler’s formula for complex number before leaving dumb comments.
Yes, it’s “2″, it’s not “i”.
Learn to read first. His handwriting is not THAT bad; your eyesight is.
HOW IS IT AN i???????
2′s do not have dots above them, nor do they have curly taily bits poking out the right hand side…
Not true! The inbred 2s have the curly taily bits…
But don’t ask me how I came about that information.
Don’t use my name when you’re writing nonsense, you prick!
Because it’s such an unusual name.
erm, it’s an eye, maybe you need to wipe your glasses?
ffyyyyy omgshitzlolor —— hahahahah funny
OMGWTFLOLKFCBBQUNICEFNBACIAROFLMAOIIRCYMMVIMHONAACP —– I am a pretty snowflake!
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
It does matter if it’s a mathematical error. If you’re trying to prove to someone that they’re idiots, you better not be an idiot…. oooh sparkly!
oooh fluffy!
Ultimate WIN
Hi, Franc. I am iron man.
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
yes, this has alredy been discussed, also some people are really blind
Hike Connor, for example. use your desktop zoom (with fractal/wavelet interpolation of course) to see exactly what he wrote.
Oh, you do not even have a desktop zoom? Then shut up, when real computer users talk!
Ch, and: Compiz-Fusion FTW!
No we’re not!
Oh wait….
It’s a check for 0.2 cents, not 2 cents. And that’s exactly what makes this picture funny.
Ehhhhhhhh…post editing FTL. This is what happens when I’m on the internet at 7 am…
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.)
or .2 cents, depending if you ask a sane person or some finance guy at verizon
I’m with him on this one, you can’t call it a win if you can’t spell pi
Randall, get out of my banking system!
Bored now.
if it’s the same guy who had the verizon math fail it would make cents for it to be written out for $.002
I see what you did there!
It’s the author of xkcd making fun of the verizon math incident.
Sucky sucky only e^(2\pi i) dolla.
Would you like to go to my room bouncy bouncy?
I am no longer infected.
That’s what she said.
Fail!
e^(i*pi) = -1, so total sum = $0.002, not $536.49.
Rather old but still epic win on the part of Randall… Very fail on the part of the idiot who added the calculation.
And in that original larger picture of the cheque, it’s even more clearly an ‘i’, not a ’2′.
Listen, an i for an i and a 2 for a 2 will only leave us 2thless and blind!
and then you’ll be ripe for the picking
solve that verizon, i dare you, i double dare you
this will spice up my training for the math exam
Please, choose another username. This one is toxic.
Why so confrontational? I’m sure we con work things out!
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.
Oh, and why is the sum to infinity from 1/2^n = 1?
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
i dont think this is something you could call an correct argument. sorry but it kinda fails.
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?
*onder de indruk*
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 ^^
I would reserve that particular phrase for when your (imaginary) wife says: “Not now, gnaa, I have a headache”.
Ah, so you are a constructivist, a la Brouwer, and you do not allow for actual infinities. I see.
Is that a valid recursive proof? Kinda neat if so.
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.
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.
Ok scratch that. I didn’t see that n=1 at start. My bad.
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.
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
The guy got his full refund 3 a little over 2 years ago. There is actualy a 22 minuit more painfull version you can find on the web where he talks to 5 people who still dont understand the math and eventualy offer him a %50 credit.
omit (3)*
I imagine she told everyone she knows and was laughing about it with her coworkers all day. Her extended family is probably sick of hearing about it by now.
I’ll cash it for ya….
Daily gif blog
DB
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
It’s actually exactly 1. Crazy, right?!
no, it’s close but it never reaches 1.
In general, 1+x+x^2+x^3+…=1/(1-x)
So in a sense 1-1+1-1+1-1+…=1/2
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
“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.
That only works when |x| is strictly less than 1.
actually since it goes to infinity it does equal exactly 1.
And remember folks .9 repeating = 1
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.
First!!!!!!!!!!!!!!
Oh, w8,
number f@il.
Good on ya mate.
;D
That’s a reverse Haxored. Very complicated trick to perform. 9,5 points!
Hahahahahaha!
check win, failblog failest of all fails. The text below the picture is so wrong my eyes hurt. It’s check for 0.002.
Pi spelling fail?
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$.
Math sucks.
Chemy takes it up the pooper.
actualle the sum of 1/2^n is 0 so there was a fail in the explination ^^
There is a fail in the explanation, but that’s not it. You are wrong.
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 …
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/
The real fail is the caption at the bottom where the math is wrong. The *real* amount is for $.002
well, maybe the caption was by verizon? you know how they do math.
Yeah, in the actual check it says e^i*pi not 2*pi.
is this in dollar or in cents? oh wait, its verizon, it doesnt matter if its dollar or cents.
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!
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.
I went to high school with this guy. He is a douchebag. But XKCD is funny.
XKCD = FAIL?
…
MY WORLD JUST GOT TURNED UPSIDE DOWN!
Anyone who would trust the math skills of someone who writes Pi as “pie” has failed as far as I’m concerned.
indeed
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.
As others have commented this is an epic math fail. Whoever did the caption needs to learn high school math.
Actually, that’s Calculus, which is taught in college.
Unless you are smart, in which case it’s taught in high school.
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.
Wow, for a moment there it looked as if your avatar turned red and showed a lot of pointy teeth!
I just giggled for about 10 minutes at the
“Hey dipshit, how about you blow me.”
The picture may be a little too far away, but I was also foaming at the mouth.
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.
Umm, Exp[i*pi] = -1 is not really calculus… Neither is spelling pi correctly
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.
last time i checked, you can’t get higher than a 4.0 GPA. I’m calling shenanigans on that.
*squeeze*
Nah, Calculus is the professor with the little beard and the teeny hat from Tintin. This is some kind of weird sum stuff.
*SQUEEZE* Oh Moomin, you always brighten up my day!
*cartwheels*
And how are you today mr. cuddles?
Isn’t e^(ipi) marvellous? The three most nonsensical numbers in existence combine to form -1?
I’m doing well. I can’t wait for this day to be done though. How are you today Mikey?
Glad to hear it! Me too.
I have the uneasy feeling that something, somewhere, has gone horribly wrong.
Is “easy” an antonym of “uneasy”?
Somebody’s getting his cell phone service canceled…
i like how he spelled pi wrong
this has to be the guy from the verizon operator argument. more power to ya.
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
*stops being retarded.*
-WhatIKnow
I refuse to be controlled!
*puts pants on head and walks into wall*
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.
Fail. \exp(i \pi) = -1.
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.
UR rite
nice math!
must be european *LOL*
Except he’s written n=1…so no, n does not include 0.
Check here for a larger image: http://xkcd.com/verizon/
It seems to be 2.002, then
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.
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
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
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!
*punching into a calculator*
So, what number do I divide that by so it spells BOOBLESS on my calculator?
7.3 I believe.
I’ll just trust that all of you math nerds have this one covered.
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?
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.
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.
Who writes a check these days?
Honestly.
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!
I love smart people.
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).
\-|–
Holy crap I thought I was the only one who noticed that.
MATH FAIL: e^(pi*i) = -1. That check is written for .002 cents.
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.
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
That’s a pretty sweet win there…
I doubt that I would have figured it out.
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.
sense of humor fail?
obvious win
Would that cheque be valid?
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.
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!!!!!!!!!
that man is my hero.
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.
Thank you. I was just gonna say that. It obviously reads e^(i pi), not e^(2 pi)
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.
This is what you get when nerds try to be funny.
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
http://xkcd.com/verizon/ for a larger pic so you can clearly see its e^(i*pi)
I always preferred Geography
HAHA, me too.
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/
Thank you.
No kidding. WTF is funny about a $500 check to Verizon?
Most people just suck at math, Verizon employee or not.
Idiots, there’s no limit. That’s a sequence that converges to 1.
Idiot. Thats what the term “limit” means. The limit is the point of convergence.
ZOMG! RANDALL!
*big fan*
This check is epic win…
Randal Munroe GET OUT OF MY HEAD!
No surprise someone trying to show off their math skills misinterpreted this all wrong.
is this a failblog fail ?
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.
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.
I was just thinking that, actually – “How could 1 over an infinitely large number be anything but an infinitesimally small number? Oh yeah, ‘cuz people are dumb.”
It’s the limit sum.
Does anyone not know that 1/infinity equals zero?
NaN
I think this man is my new hero.
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)
Pretty sure that Riemann sum =’s 0 not 1.
1/infinity =/= 1
1/infinity => 0
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.
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…
ok… this is for $.002! change the caption! eulers identity =1 – 1 so .002…. get it straight!
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.
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.
more like check writing fail. what a loser.
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.
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.
Damn sum not limit riiiiiiiighhhhtt
My b
The real (not imaginary) Fail here is that his check cost more than the $0.002 for which it was made out…
But I bet the laugh he got out of it was priceless. *thinks of a mastercard ad spoof*
*sigh*
Thank you, witty regulars, for making all that scrolling^^^ past the MATH WARS^^^ worth at least a chuckle or .002!
That sum adds up to 2 tards. Its a geometric series pshhhh
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.
A little part of me died.
This thing is retarded. whoever did the math can’t read.
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!
) *steps off soapbox*
Lol @ “Pie”
This is really a fail of failblog math skill
The Fail in this case is the caption text below.
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!).
e ^ (2 * pie) would be quite a lot of cake. Maybe Verizon haz a birzeday?
It would have been a win if Verizon had posted the check.
No amount of “positive teacher talk” could ever inspire me to learn calculus, but this has.
you can clearly see it’s i*(pi) on the site of the guy who wrote the
check http://xkcd.com/verizon/
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.
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.
haha i work for bb&t
this is probably one of the better things one would have to deal with
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?
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.
Euler would be upset his formula was used on a check!
pi spelling fail
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.
Excellent work Mr. Munroe… Enjoyed the memo also, very curious as to whether they actually accepted this payment and whether the bank cleared it…
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
Don’t you guys have a Star Trek convention or something to go to?
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.
OMG already! Didn’t you read ANY of the comments? It’s between the “X” and the “R”!!!!!
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.
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
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?
Because your evaluating complex numbers to complex powers.
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..
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.
1..inf that is.
Clearly you aren’t a Math Nerd. It isn’t a limit; it’s a summation.
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.
Oh, yeah? Well, what’s purple and commutes?
An abelian grape! I’m glad someone else knows this joke!
Yeah, good ol’ Mr. Schaeffer, God rest his soul…I never got a chance to go back and tell him I finally got it!
Ah, but what’s yellow and equivalent to the axiom of choice?
Zorn’s Lemon!
And yes, the math below is wrong. I’m in 8th grade and I knew that….. LOL. It’s equal to .002.
Oh! To the people who say it’s 2(pi):
http://xkcd.com/verizon/ The original.
Actually, he didn’t include the “lim” notation in front of the sigma. So really that doesn’t work out.
A limit and a summation are two different things. It works out fine.
Epic Epic WIN!!!!
Actually, this check isn’t even legal. A negotiable instrument must be made for a specific amount.
Nice work, except that he wrote (2pie) instead of (2pi).
if the n is wrote a bit larger and become 2n instead of 2^n
he will be broke as it is infinity
Nice dude!
You guys do realize that the sum is worth 2 and not 1, right ?
Nope, that sum converges at 1.
That’s and ‘i’ not a ’2′… Reading fail.
He misspelled Pi.
This is amazing
Annotation/image manipulation FAIL.
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.
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.
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.
haha “computation fail”!
Actually, it reads e to the quantity pi times /i/, which is equal to -1. So the amount is actually only $.002.
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 !!
olol fail
read the other comments
FOR THE LOVE OF GOD USE A TI89 CALCULATOR THE SUM IS 1!!!!! A SUM AND A LIMIT IS NOT THE SAME THING.
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.
Nerd alert.
will you people do my homework?
Now, they cash the cheque – after they get someone to decipher it
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
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.
i dont care if its right or wrong, this is freaking hysterical!
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.
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.
if i got that i would just be like “No.”
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.
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
Is that e^(2Pi) or e^(i Pi)?
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
=)
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.)
IS NOT A LIMIT IS A SUM, SUUUUM!!!!!!!!!!!!!!!! FROM 1 TO INFINITY = 1!!!!!!!!!!!!!!!!!!!
EPIC WIN!!!!!!!!!!
This FAILs for the misspelling of “pi” in the explination of the equation.
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.
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
you guys actually give a shit about this? FAIL.
Explanation Fail: pie instead of pi. Nicely done.
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.
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
Does anyone else love how in the explanation they wrote pie instead of pi?
get a life
Any of you guys (and maybe girls) ever watch The Big Bang Theory on Monday nights? Just curious.
YEAH. and im a girl
$536.49 for a Verizon bill?? More like Verizon win.
heh, I love how he gets semi-technical with the math, and then misspells pi…. just made my day XD
Eh he read the check wrong + bombed on the math stuff too XD So… Win + Super-Fail?
……….freaking smart people………
D
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.
TI89 YOU GUYS!
with all these ppl commenting, i turned into a FAIL.
I think it says
e^i*Pi
that is equal to -1
lim(1/2^n) when n is approaching infinity is 0, not 1..
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.
WHen the n is approaching 0, then the limit becomes 1..
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…
test
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.
WHAT CALCULATOR ARE YOU USING? AND CHECK THAT YOU TYPED EVERYTHING RIGHT.
i would give them money, not math
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
it’s a 3…
@ “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.
thats hot.
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
Correction
It is sum that essentially is 1 after the first 10 terms.
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…
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!!
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.
its own*
It’s actually e^(2 pi e) which is $26152833.54. So it looks like Verizon won.
NO.
Is anyone even reading these comments anymore?
YES.
what now?
Is its teh cherry pi?
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!
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.
And the amount of time it took the loser to work this out is completely non-chargeable to Verizon. What a WIN…
Not…
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.
calculus win!
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!
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
Pi spelling fail…
i wonder if the bank would accept it
of course they would they would just call the guy first.
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?’
Math Computed:
http://www.wolframalpha.com/input/?i=0.002+%2B+e%5E%282pi%29+%2B+%28sum+1%2F%282%5En%29%2C+n+%3D+1+to+infinity%29
http://www.wolframalpha.com/input/?i=0.002+%2B+e%5E%28i*pi%29+%2B+%28sum+1%2F%282%5En%29%2C+n+%3D+1+to+infinity%29
Fixed that for you.
it’s e^(i*pi), not e^(2*pi)
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.
Word, dude. The actual fail of this pic is the caption.
Equation:
{failblog/Winblog-vrizon communication+the stupidity of bush(which equal to infinity BTW)=Comment……
I just love this one…
very clever.
Thanks for another excellent post. The place else may just anybody get that kind of info in such an ideal method of writing? I’ve a presentation next week, and I am at the look for such info.
Just want to say your article is as astonishing. The clearness for your post is simply nice and i could suppose you’re an expert on this subject. Fine with your permission let me to clutch your RSS feed to stay updated with impending post. Thank you one million and please keep up the rewarding work.