An infinite number of mathematicians walk into a bar…
November 20th, 2008 Posted in Physics Humor
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”
November 26th, 2008 at 5:55 pm
Haha, good one.
November 27th, 2008 at 6:26 am
Go bartender.
November 27th, 2008 at 7:30 pm
Stupid bartender. He didn’t even wait for everyone else to order.
November 27th, 2008 at 8:21 pm
Bartender FTW!
November 27th, 2008 at 9:44 pm
infinite series ftw.
November 28th, 2008 at 12:33 am
I don’t get it.
November 28th, 2008 at 1:02 am
I cant understand what you are trying…but i like the quotes….
November 28th, 2008 at 3:00 am
would someone please explain this to me please? e-mail me at a.gollings9845@student.leedsmet.ac.uk
November 28th, 2008 at 3:33 am
the bartender gave them to much beer! lol. lol.
November 28th, 2008 at 5:37 am
Sn=a/(1-r)
=1/(1-.5)
=1/.5
=2
November 28th, 2008 at 5:49 am
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
November 28th, 2008 at 7:03 am
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.
November 28th, 2008 at 8:00 am
sum of infinite terms = a / ( 1- r) = 1 ( 1- 0.5) = 2
November 28th, 2008 at 8:54 am
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!
November 28th, 2008 at 11:34 am
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?
November 28th, 2008 at 12:45 pm
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..
November 28th, 2008 at 5:11 pm
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.
November 29th, 2008 at 5:54 am
It’s much funnier if the bartender’s reaction is less harsh, i.e. “the bartender rolls his eyes and pours two beers”.
November 29th, 2008 at 7:57 am
Surely the logical last line is “You’re all idiots. Here’s two beers. Have the rest on the house” ?
November 29th, 2008 at 2:19 pm
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
November 29th, 2008 at 5:23 pm
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.
November 29th, 2008 at 5:25 pm
Sorry i reread the statement and i confused ‘third’ and ‘three’, the bartender is not stupid…
November 30th, 2008 at 7:43 pm
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.
November 30th, 2008 at 7:49 pm
ok the rectangle didn’t show properly.
________________________________
|…………….|……………|
|……1/2…….|……………|
|…………….|……………|
|________________|……_1_……|
|……..|.1/8…|……………|
|..1/4…|_______|……………|
|……..|1/.|…|……………|
|________|_16|___|_______________|
November 30th, 2008 at 7:50 pm
ok i give up….
November 30th, 2008 at 7:51 pm
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.
December 1st, 2008 at 6:57 pm
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?
December 1st, 2008 at 9:27 pm
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!
December 2nd, 2008 at 10:28 am
OMG!
The joke was funny but the responses are even funnier. I have to mail this to every math teacher I know!
December 2nd, 2008 at 10:31 am
[...] [via] [...]
December 2nd, 2008 at 4:22 pm
It’s nonsense, unless you are saying the bar is infinitely big, or the mathematicians are infinitely small?
December 2nd, 2008 at 9:39 pm
that wasn’t really funny… the bartender is the idiot
December 3rd, 2008 at 1:34 am
Kwan that was an awesome proof
December 3rd, 2008 at 8:02 am
i don’t understand :(((
December 3rd, 2008 at 4:51 pm
I would like a beer
December 4th, 2008 at 2:55 am
yeah. Kwan’s proof is cool as f***. Simple yet potent.
December 4th, 2008 at 10:19 pm
seems rather presumptuous, the bartender only heard three orders. 1, 1/2 1/4
maybe the fourth guy orders 1/7th of a beer.
December 5th, 2008 at 4:10 am
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!!!!!!
December 5th, 2008 at 8:14 pm
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.
December 6th, 2008 at 4:08 am
its called a half-life, or radioactive decay
December 6th, 2008 at 8:33 am
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…..
December 8th, 2008 at 11:34 am
You’re all mathematicians and should keep away from bars.
December 8th, 2008 at 10:01 pm
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.
December 9th, 2008 at 5:14 am
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
December 12th, 2008 at 7:07 am
Envision infinite beer.
Mmmmm
December 13th, 2008 at 3:32 pm
[...] An infinite number of mathematicians walk into a bar… [...]
December 18th, 2008 at 1:10 pm
I like the funny addition by Cadmonkey!
Cool!
December 19th, 2008 at 6:01 am
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…
January 9th, 2009 at 1:44 pm
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January 30th, 2009 at 4:22 pm
I rofled.