Nov 20, 2008
Posted by Sunny Kalara in Physics Humor | 53 Comments
An infinite number of mathematicians walk into a bar…
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
Funny addition by CadMonkey at StumbleUpon
…then they asked for separate tabs…”An infinite number of mathematicians get thrown out of a bar”
Talk Like a Physicist
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Haha, good one. ;)
Go bartender.
Stupid bartender. He didn’t even wait for everyone else to order.
Bartender FTW!
infinite series ftw.
I don’t get it.
I cant understand what you are trying…but i like the quotes….
would someone please explain this to me please? e-mail me at a.gollings9845@student.leedsmet.ac.uk
the bartender gave them to much beer! lol. lol.
Sn=a/(1-r)
=1/(1-.5)
=1/.5
=2
this is funny because in an infinite series that starts at 1 and has the amount halved every time, the total sum approaches 2 – but never reaches it. So in this the bartender cut out the middle man and just poured 2 glasses
The 2nd mathmatician orders 1/2 a beer, the third 1/4th of a beer and it is safe to assume that the 4th will order 1/8th. Each successive mathmatician is ordering n/2 of a beer where n is the previous mathmatician’s beer amount. This is the classic infinite geometric series with a finite sum of 1. Counting the beer the very first mathmatician ordered: 1+1 = 2.
There. I explained it for all you people who aren’t geeks. shame on you.
sum of infinite terms = a / ( 1- r) = 1 ( 1- 0.5) = 2
That’s absolutely hilar-e-ous!
One way to understand the problem is this: if an infinite series of patrons place orders for beer, the first ordering one beer and each of the subsequent patrons ordering half the quantity of his predecessor, we would have a ‘total’ amount of beer according to the infinite series:
1 1 1 1
— + — + — + —
1 2 4 8 , . . .
The first order constitutes a whole beer. But since we then beginning slashing the quantity of each new order in half, we can see that, even expanded outward to infinity, the sum of all the parts of the series will approach but never equal two whole beers. This is essentially because any whole number can be divided into an infinite number of parts. One half, plus half of a half, plus half of a half of a half, etc., will never add up to equal a whole. Therefore, by pouring two beers, the bartender assures more than enough beer than this infinite series of mathematicians could ever consume!
Really witty; great joke!
the infinite number of remaining mathematicians would continue to order a smaller fraction of a beer infinitely, but never adding up to more than one, so the bartender only needs to pour two beers and let them divide the second into the smaller fractions..get it?
X = 1 + 1/2 + 1/4 + 1/8 + …
2X = 2 + 1 + 1/2 + 1/4 + …
2X = 2 + ( 1 + 1/2 + 1/4 + 1/8 + …)
2X = 2 + ( X )
X = 2
I.e., the sum of the series is 2..
1/2 + 1/3 + 1/4 = 13/12
Did you mean 1/2, 1/4, 1/8, 1/16,…?
As in 1/2 + 1/4 + 1/8 + … 1/(2^n)?
Just wondering.
It’s much funnier if the bartender’s reaction is less harsh, i.e. “the bartender rolls his eyes and pours two beers”.
Surely the logical last line is “You’re all idiots. Here’s two beers. Have the rest on the house” ?
A couple of observations.
1/1) so many people explained the reasoning behind the joke, which defeats the purpose (i.e. You/we are a bunch of geeks)
1/2) Who orders only half a beer? Is the vessel so large you can only drink half?
1/4)Or are Mathematicians a depressing lot in that the glass is rarely more than half full?
1/8) Or can you split a beer atom to create bubbles in your brew?
Cheers
The infinite sum of 1+1/2+1/4+… goes to 2. But here it’s the sum 1+1/2+1/3+1/4+…, which is the harmonic series, this diverges to infinity. The bartender is is stupid.
See wikipedia: Harmonic series, harmonic number.
Sorry i reread the statement and i confused ‘third’ and ‘three’, the bartender is not stupid…
Have a look at this badly drawn rectangle …
____________________
| | |
| 1/2 | |
|__________| |
| | 1/8| 1 |
| 1/4 |–|-| |
|_____|__|_|_________|
Think about the area of the rectangle, I know it’s not accurate but let’s pretend it’s 1 unit high by 2 units wide.
The total area is therefore 2 sq units. Having halved the rectangle you can see the area on the right is 1 sq unit, dividing what’s left again gives you another 1/2 sq unit and again giving 1/4 and again 1/8 and again and again …
We know the total area is 2 sq units and we can see that if we keep dividing the shape in half we get 1, 1/2, 1/4, 1/8, 1/16 … It’s clear from this that if we continue to divide in half the total area will (if we could reach infinity) be
2 and no more than 2.
ok the rectangle didn’t show properly. :-(
________________________________
|…………….|……………|
|……1/2…….|……………|
|…………….|……………|
|________________|……_1_……|
|……..|.1/8…|……………|
|..1/4…|_______|……………|
|……..|1/.|…|……………|
|________|_16|___|_______________|
ok i give up….
Actually you are all idiots. The amount of mathematicians in existence is finite. Mathematicians always gloss over the obvious to achieve an end. I live in reality on the planet Earth.
i just feel bad for the guys that have to split the second beer. after like the 16th mathematician all you’re really getting is mathematician backwash, and who wants that?
As Calculus shows us, as the function approaches infinity, the result will approach 2 but never reach it. So, lapper220 is correct in saying that “the rest is on the house.” At some point a mathematician, far down the line, will have to order a molecule of beer meaning the next one would have to order half a molecule of beer. Half a molecule of beer is no longer beer. Hah!
OMG!
The joke was funny but the responses are even funnier. I have to mail this to every math teacher I know!
It’s nonsense, unless you are saying the bar is infinitely big, or the mathematicians are infinitely small?
that wasn’t really funny… the bartender is the idiot
Kwan that was an awesome proof
i don’t understand :(((
I would like a beer
yeah. Kwan’s proof is cool as f***. Simple yet potent.
seems rather presumptuous, the bartender only heard three orders. 1, 1/2 1/4
maybe the fourth guy orders 1/7th of a beer.
seeing as the infinite amount of mathematicians ordering exponentially smaller amounts of beer, technically two full glasses are more than they would have all collectively ordered. However, i’m sure the extra bit of beer was worth it to the bartender who didn’t have to pour increasingly less amounts of liquid.
aieeeeee!!!!!!
Cool Method Kwan! I guess you know it, but just in case:
You can only use this method if you have already reasoned that the infinite sum converges.
its called a half-life, or radioactive decay
I tried this as a warm up question to some students, and one, who has a reputation for being shall be say not the brightest, gave the best answer I’ve heard yet…..
“well, they would need an infinity of beer”
Me patiently explaining “No, you see you’ll never fill the second pint…”
“Oh, I get that, BUT THEY NEED A GLASS EACH; DON’T THEY?”
Shut me right up…..
You’re all mathematicians and should keep away from bars.
Inconsiderate bartender! Maybe they didn’t want to share germs…if they are that much of geeks they problem don’t want to catch anything lol. Plus, they might want separate tabs…if I were the bartender I would charge them like a psychologists…charge them each for a full beer lol.
if the bartender knew the branch of statistics, then he would know that previous observations hold no bearing on immediate future observations and thus should not jump to such a hasty conclusion
Envision infinite beer.
Mmmmm
I like the funny addition by Cadmonkey!
Cool!
I think it’s an amusing math joke but why the bartender calls them all idiots is rather arbitrary. Obviously they know that 2 beers is the result of how much beer will be poured but the bartender makes it sound as if they didn’t know that…
I rofled.
I laughed even harder at skitsomatic’s post lol.
Imagine if the mathematicians gets infinity smaller as well.
This joke is so funny! Very Monty Python I might say. Hahaha! :))
Thank you guys!