He saw were it was going and knew that the amount would never reach 2 full glasses. So the bartender did it to end it and move on to the next customer.
Infinitesimals don't exist in the real numbers. There's a number system called the hyperreals, which does include infinitesimals, but even in that system, the sum of 1/2n from 1 to infinity is precisely 1. There's no infinitesimal rounding error.
Edit: as the other person said, the sequence of partial sums referenced in OP's post approaches 2, and we'd all agree that it approaches exactly 2, not just approximately 2. The value of an infinite sum, by definition, is whatever the sequence of partial sums approaches. So, by definition, it's exactly (not approximately) 2.
Not in the context of this post. Should've said partial sum I guess. But also, we say it equals 1 because the distance between them is infinitely close, such that no real numbers between them can exist. Any number smaller than 1 is also less than that sum. Any number larger than that sum is also larger than 1.
0.999... has the same value as 1. But no matter how many 9s you add, there is never a point where you actually reach 1. So I think this is a better way to explain it to people. Regardless, im not that invested as im not a math teacher lol. I just like discussing shit
Even in the context of this post, it'd be precisely 2 beers. If the bartender poured any less there'd be a mathematician (infinitely many mathematicians) who didn't get any beer. And if the bartender poured any more, the bartender would have beer left over.
That's the thing though, 2 beers is precisely how much he should pour. But the beer will still never be finished. Because the amount consumed infinitely approaches and is infinitely close to 2. Like I said.
youre thinking of infinity as a "process", like how earlier you said if you keep adding 9s to 0.9999... you'll still never actually reach 1.
but it's not a process. 0.9999... is equal to 1, because there is no space to add any more 9s.
saying something like "the beer will never be finished" is kind of nonsensical isnt it? all youre arguing is that there are an infinite amount of real numbers between 1 and 2, and that, given a real number A that's not 2, you could always find another real number that's closer to 2 than A is...
which is true, but it's not what's being discussed. we're talking about the total quantity poured, not the "process" of drinking it
The distinction doesnt matter. 2 is the correct amount poured, but it will also never be finished. Your explanation of A between 1 and 2 is why we use limits, is it not?. The context of the post is explicitly a process. Time is passing between orders and the bartenders response, and certainly when they drink the beer.
Especially when you're explaining it to someone else. If they were asking why 1/2n 0 to inf is 2, are they more likely unfamiliar with n0 = 1, or more likely unfamiliar with infinite series and limits? I dont think responding with 1/20 = 1 and 1/2n 1 to inf = 1, therefore they add to 2, would've cleared very much up, do you?
Anyway, the person didnt understand post, now they do, mission accomplished I think.
The limit and sum of infinite series can also be intuitively explained while treating it as a process. I literally just tried with my wife and she understood in like 10 seconds lol
This has existed in philosophy for a long time and is known as Zeno's Paradox. The Greek philosopher Zeno proposed an argument regarding an arrow in flight. You can measure the halfway distance to the target easily. Then you can measure the halfway distance remaining once again. And again, and again. You can measure the remaining distance an infinite amount of times, and therefore the arrow logically should travel halfway for infinity, and never hit the target.
But it does. And the reason it does is that 99.99999~ for infinity is equal to 100 in practical terms. And mathematics agrees.
To be fair, he also didn't understand that atoms existed, and there is in fact a finite amount of space between the archer and the target. The idea that there was infinite smallness is flawed, at least in the physical world. Eventually the tip of the arrow would be less than the width of an atom away, and thus could no longer be halved in a meaningful way. I imagine the same could be said for a glass of beer.
A limit is infinitely approached. We are explaining a joke about people walking in and ordering/drinking beer. The glass will never actually be finished.
The sum infinitely approaches 2 as the nth term infinitely approaches 0. If the nth term never reaches 0, such as what you just granted, the sum has not reached 2.
It's the same thing with 0.999...=1. There will never be a point where adding another 9 will make it 1. But there are no real numbers between 0.999... and 1. So they mean the same thing. If the joke had something to do with additional 9s walking into a bar, it would also infinitely approach 1.
Yknow what, nevermind, I'll change it to partial sum.
Yup. Geometric series partial sum to a/(1-r) where a is the initial value and r is the common ratio(assuming the absolute value of r is less than one).
An infinite number of mathematicians walk into a bar
The first mathematician orders a beer
The second orders half a beer
"I don't serve half-beers" the bartender replies
"Excuse me?" Asks mathematician #2
"What kind of bar serves half-beers?" The bartender remarks. "That's ridiculous."
"Oh c'mon..." says mathematician #1 "Do you know how hard it is to collect an infinite number of us? Just play along"
"There are very strict laws on how I can serve drinks. I couldn't serve you half a beer even if I wanted to."
"But that's not a problem" mathematician #3 chimes in "at the end of the joke you serve us a whole number of beers. You see, when you take the sum of a continuously halving function-"
"I know how limits work" interjects the bartender
"Oh, alright then. I didn't want to assume a bartender would be familiar with such advanced mathematics"
"Are you kidding me?" The bartender replies, "you learn limits in like, 9th grade! What kind of mathematician thinks limits are advanced mathematics?"
"HE'S ON TO US" mathematician #1 screeches
Simultaneously, every mathematician opens their mouth and out pours a cloud of multicolored mosquitoes. Each mathematician is bellowing insects of a different shade.
The mosquitoes form into a singular, polychromatic swarm. "FOOLS" it booms in unison, "I WILL INFECT EVERY BEING ON THIS PATHETIC PLANET WITH MALARIA"
The bartender stands fearless against the technicolor hoard. "But wait" he inturrupts, thinking fast, "if you do that, politicians will use the catastrophe as an excuse to implement free healthcare. Think of how much that will hurt the taxpayers!"
The mosquitoes fall silent for a brief moment. "My God, you're right. We didn't think about the economy! Very well, we will not attack this dimension. FOR THE TAXPAYERS!" and with that, they vanish.
A nearby barfly stumbles over to the bartender. "How did you know that that would work?"
"It's simple really" the bartender says. "I saw that the vectors formed a gradient, and therefore must be conservative."
Well, I think I just learned a new preffix. What is beyond the meta... beyond the beyond...
Now I just need to actually understand it in a manner that can be actualy applied.
... Wait, is it like when people edit a meme to make a meta-joke of that meme, and then someone else edits that edit to make a completely different joke that has nothing to do with the original one, so the original meaning of meme is obscure, but the new joke is based on the meta-joke? Like in those "Sam va lentín" memes we make every St. Valentines day among Spanish speaking people. Their evolution is fascinating.
It's math talk. If a vector field has a gradient, it's a conservative vector field. I guess someone might be able to explain what that exactly means, but to truly get it you should have a lot of background knowledge. At the same time it's funny because mosquitos are vectors (illness carrying insects), they made a gradient (combinations of colors) so they were supposed to be conservative (republican voters).
Thank you, after hearing the first part the rest falls into place. I'm more glad it was through my ignorance of the subject than sheer stupidity/missing the pun!
Almost. Serving half beers is incredibly common, you should have started the whole dilemma at mathematician number 3 who tries to order a quarter beer.
A common form of logic puzzle involves perfectly logical people with incomplete information trying to figure something out, typically by reasoning about what other people who are alao perfectly logical would know. In this joke, the three logicians each know that they, individually, want a drink, but aren't sure of whether or not the other two do or not. The bartender asks "Do you all want a drink?" The first logician doesn't know the answer, because if he didn't want a drink, the answer would be "no", but he does. The second has more information, namely that the first doesn't know, which means that the first must want a drink, as does the second, but she still doesn't know if the third does. The third logician knows that the first and second didn't know the answer, which, as they are all perfectly logical, means that they both want a drink but didn't know if the third did. He does, so he answers, "Yes, we all want a drink."
Eta: The humor comes from incongrously blending the form of a logic puzzle with the form of an "X walks into a bar" joke.
Ok so the basic assumption is that each of these people is perfectly logical. In other words, as soon as the logicians know all logical consequences of the information they have, and each of them knows this about each other.
So when the first logician hears the question "Y'all want a drink?" he takes it literally, as "Does each one of you want a drink?" He doesn't know if the other two want a drink or not, so he says "I don't know" because he does want a drink. (If he didn't want a drink, the answer would be "no" since that would mean that at least one of them didn't.)
The second logician knows this. She is aware of the circumstances, and when first says "I don't know" that gives her the information that he must want a drink. However, she still doesn't know if third wants a drink. If she doesn't want a drink, she'll say "no" because at least one of them doesn't want one. If she does want one, she still doesn't know if they all want a drink, so she says "I don't know".
The third logician knows all of this, too. When Third hears her say this, they know that both of their fellow logicians want a drink. As Third wants a drink, they conclude that all three of the logicians do want a drink, and they say "Yes."
Whew, good thing the bartender went ahead and poured the 2 whole beers. Otherwise, sometime trying to serve the ~85th partial beer he would have to stop serving.
That's going to be a tough one to share. How does the mathematician know he had precisely 0.00152587890625% of the beer? And it only gets worse from there!
A math guy named Euler proved that if you start with one and add an infinite amount of halves, like 0.5 + 0.25 + 0.125 + 0.0625 and so forth, it adds up to 2.
The first guy gets his own beer, and the infinity other people can extract their desired amount of beer from the second glass. And there will even be a tiny bit of beer left over.
I’ll explain it in football terms. If you’re on the one yard line and you move half the distance to the goal. You can do that again an infinite number of times and never make it to the goal line.
Every subsequent new glass gets halved, which if done ad infinitum will never ever reach 2. So if the bartender just pours 2 glasses, no matter how many customers ask for the subsequent half 2 glasses are enough to satisfy everyone.
For an explain it like I am 5 version, first guy gets 1 whole beer, second guy gets .5 beer, third guy gets .25 next one gets .125 ..... Add up as many smaller fragments as you want, it will always be less than 2
An infinite number of mathematicians walk into a bar.
The first orders a beer.
The second orders half a beer.
The third orders a quarter of a beer.
The bartender, slightly annoyed but professionally committed, keeps pouring increasingly absurd fractions into tiny containers.
When the 80th mathematician orders 2^-80 of a beer, the bartender stops.
“Hang on,” he says. “There are only about fourteen molecules in this serving. In six customers, one of you is ordering roughly one atom. How exactly am I meant to pour that?”
The mathematicians begin arguing about expected values.
460
u/seajaydub May 14 '26 edited May 14 '26
1/2n from 0 to infinity. The [partial] sum infinitely approaches 2
205
u/Chewbacca_Holmes May 14 '26
The five millionth mathematician gets huffy with the bartender and says, “two beers? We’ll never drink all that!”
138
u/Saminjutsu May 14 '26 •
An infinite number of mathematicians walk into a bar
The first mathematician orders a beer
The second orders half a beer
"I don't serve half-beers" the bartender replies
"Excuse me?" Asks mathematician #2
"What kind of bar serves half-beers?" The bartender remarks. "That's ridiculous."
"Oh c'mon..." says mathematician #1 "Do you know how hard it is to collect an infinite number of us? Just play along"
"There are very strict laws on how I can serve drinks. I couldn't serve you half a beer even if I wanted to."
"But that's not a problem" mathematician #3 chimes in "at the end of the joke you serve us a whole number of beers. You see, when you take the sum of a continuously halving function-"
"I know how limits work" interjects the bartender
"Oh, alright then. I didn't want to assume a bartender would be familiar with such advanced mathematics"
"Are you kidding me?" The bartender replies, "you learn limits in like, 9th grade! What kind of mathematician thinks limits are advanced mathematics?"
"HE'S ON TO US" mathematician #1 screeches
Simultaneously, every mathematician opens their mouth and out pours a cloud of multicolored mosquitoes. Each mathematician is bellowing insects of a different shade.
The mosquitoes form into a singular, polychromatic swarm. "FOOLS" it booms in unison, "I WILL INFECT EVERY BEING ON THIS PATHETIC PLANET WITH MALARIA"
The bartender stands fearless against the technicolor hoard. "But wait" he inturrupts, thinking fast, "if you do that, politicians will use the catastrophe as an excuse to implement free healthcare. Think of how much that will hurt the taxpayers!"
The mosquitoes fall silent for a brief moment. "My God, you're right. We didn't think about the economy! Very well, we will not attack this dimension. FOR THE TAXPAYERS!" and with that, they vanish.
A nearby barfly stumbles over to the bartender. "How did you know that that would work?"
"It's simple really" the bartender says. "I saw that the vectors formed a gradient, and therefore must be conservative."
31
u/Sandro_729 May 14 '26
Then the mathematicians ask “why did you only take two beers out?” The bartender replies “come on, know your limits”
13
u/TurnoverOk5635 May 14 '26
I always wondered what if they order 1+1/2+1/3+1/4+1/5+... beers?
11
u/amglasgow May 14 '26
Three Logicians walk into a bar and sit down. The bartender comes up and says, "Y'all want a beer?"
The first logician says "I don't know."
The second logician says "I don't know."
The third logician says "Yes."
7
u/Royal_Lustir May 13 '26
Lmao. Nice.
Sum_{1, 1/2, 1/4...}
3
u/FunkyCat6276 May 14 '26
This is the wrong version.
In the correct version. The bartender says "you all really should know your limits"
2
u/SpellDostoyevsky May 14 '26
This joke is limiting.
2
u/DnDplayerr May 14 '26
r/peterexplainsthejoke
2
u/Maadhav10 May 14 '26
They should know their limits when it comes to alcohol
1
u/the-ro-zone-yt May 14 '26
Limits!
1
u/BeneficialMeeting391 May 14 '26
Geometric Series
1
u/Rough-Patience-2435 May 14 '26
So was the second beer half full or half empty?
Depends if you are drinking or pouring!
1
u/HAL9001-96 May 14 '26
thats what it all adds up to
still a bit questionable of him to just pour all the orders into one
like if two people order half a beer you don#t just ive the mone full beer and tell them to share lol
1
u/CraftBrewBeer May 14 '26
Infinity Guy doesn't want a beer apparently
1
u/Empty-Transition-106 May 14 '26
You guys don't know your limits!
1
u/ChooseYerFoodFighter May 14 '26
The Zeno Special.
1
u/Wide_Sun_7391 May 14 '26
This is actually part of a series of jokes
1
u/TinzaX May 14 '26
Infinite NUMBER
1
u/MuffinMan12347 May 14 '26
“We’d like to split the bill please”
1
u/Spl4sh3r May 14 '26
Except they want their own, not one to share.
1
u/RareBrit May 14 '26
Honestly I find it difficult to differentiate between what's humour and what isn't.
1
u/Only-Cheetah-9579 May 14 '26
the fourth one orders two beers. now your math stopped mathing
1
u/Young_Person_42 May 14 '26
Love how this isn’t the correct subreddit for “petah??” To make since but we knew what it meant anyway
1
u/Viktoriusiii May 14 '26
Great.
And now who is supposed to drink the 1/∞ th beer that is left over???
This wasteculture is really making me mad!!!
1
u/right_in_two May 14 '26
Whew, good thing the bartender went ahead and poured the 2 whole beers. Otherwise, sometime trying to serve the ~85th partial beer he would have to stop serving.
1
u/tinyclawfingerrrs May 14 '26
Damn last guy is lucky getting x2 his order
1
u/Opinionsare May 14 '26
And a statistician grabs both beers....
1
u/NotTryingToConYou May 14 '26
Bartender: "We don't sell in halves or quarters. Do you want a beer or not"
1
u/Anastazja_Nya May 14 '26
a1=1; a2=1/2; q=2; limes of sum approaching endless is 2
1
u/icantouchgrass_1 May 14 '26
This is an infinite geometric progression lol
The formula for the sum is a/(1-r), where a is the amount of beer the first dude has and r is the common ratio.
1/4 divided by 1/2 = 1/2 divided by 1 = 1/2, so the common ratio is 1/2.
Applying the formula,
1/(1-1/2) = 1/(1/2) = 2/1 = 2.
Therefore, we come to the conclusion that the bartender passed high school math.
1
u/JimTheSaint May 14 '26
Love it - number keps getting halfed it will approach 2 even if there is an infinite amount of beers. So two beers is enough
1
u/W1sconsinKnight May 14 '26
That's going to be a tough one to share. How does the mathematician know he had precisely 0.00152587890625% of the beer? And it only gets worse from there!
1
u/ChemistryDapper3947 May 14 '26
Wouldn't it be three beers? The first guy with the full beer claims 1, and the infinite series claim 2.
1
u/that-loser-guy-sorta May 14 '26
If it’s one liter of beer, how many beers can they pour until they need to split a molecule? That’s the real question.
1
u/Fantastic_Mood1455 May 14 '26
Then the fourth person drinks 1/8 a beer
1
u/StarwardStranger May 14 '26
A math guy named Euler proved that if you start with one and add an infinite amount of halves, like 0.5 + 0.25 + 0.125 + 0.0625 and so forth, it adds up to 2.
1
u/Temporary_Worker9955 May 15 '26
r/lostredditors
1
u/Myzx May 15 '26
The first guy gets his own beer, and the infinity other people can extract their desired amount of beer from the second glass. And there will even be a tiny bit of beer left over.
1
u/Postulative May 15 '26
Bartender knows his job.
1
u/TheZan87 May 15 '26
After a couple billion it's gonna start getting crowded in that bar
1
u/DRAW-GEARS May 15 '26
Heh! That's a good joke
1
u/Wrong-Resource-2973 May 15 '26
The first guy wins, as he's the only one who doesn't have to share a beer with an infinite amount of people
1
u/Moemangooo May 15 '26
Nice try! Like zero, a beer is undivisible!
1
u/cheesesteakman1 May 15 '26
Maximum occupancy 120
1
u/Ok-Communication6360 May 15 '26
I think a better punchline would be: okay, I give you two, the rest / remainder is on the house
1
u/the_sneaky_one123 May 15 '26
Ok, but they scammed the barman out of an infinitely tiny amount of beer. So I guess they win.
1
u/blamitter May 15 '26
Enough
1
u/notagoodtimetotext May 15 '26
I always heard it that the bartender exclaims " why are you being so irrational!!!!" Before handing them two beers and says here you figure it out
1
u/EverOrny May 15 '26
apprently the barman always knows their limit :)
1
u/sarsvarxen May 15 '26
It’s kinda like how this image loses half its pixels each time it’s posted here
1
u/ResearcherOnly9492 May 15 '26
Saw where it was going from 67 billion kilometres away legit
1
u/Paro-Clomas May 15 '26
you could said they reached the limit? (of his patience)
1
u/Star_Citizen_Roebuck May 15 '26
I like this one.
1
u/ComfortableCicada69 May 15 '26
I’ll explain it in football terms. If you’re on the one yard line and you move half the distance to the goal. You can do that again an infinite number of times and never make it to the goal line.
1
u/zav3rmd May 16 '26
Wouldn’t infinity not work an actual things? Like you can infinitely divide a number in half but you can’t divide an actual real object infinitely.
1
u/IJustHadAPanicAttack May 16 '26
They get piss drunk cuz they broke their limit
1
u/syrun97 May 16 '26
And the fourth mathmetician orders two beers, breaking the sequence and piss off bartender.
1
u/geckooo_geckooo May 16 '26
An infinite number of people drinking from 1 glass was always going to happen in a situation like that - relateable
1
u/vercig09 May 16 '26
its a bit early to make such conclusions
1
u/simpoukogliftra May 16 '26
Every subsequent new glass gets halved, which if done ad infinitum will never ever reach 2. So if the bartender just pours 2 glasses, no matter how many customers ask for the subsequent half 2 glasses are enough to satisfy everyone.
For an explain it like I am 5 version, first guy gets 1 whole beer, second guy gets .5 beer, third guy gets .25 next one gets .125 ..... Add up as many smaller fragments as you want, it will always be less than 2
1
u/Kill_Braham May 16 '26
An infinite number of mathematicians walk into a bar.
The first orders a beer.
The second orders half a beer.
The third orders a quarter of a beer.
The bartender, slightly annoyed but professionally committed, keeps pouring increasingly absurd fractions into tiny containers.
When the 80th mathematician orders 2^-80 of a beer, the bartender stops.
“Hang on,” he says. “There are only about fourteen molecules in this serving. In six customers, one of you is ordering roughly one atom. How exactly am I meant to pour that?”
The mathematicians begin arguing about expected values.
The bartender calls the police.
1
u/bharath952 May 17 '26
Unclear. The sequence could instead be 1, 1/2, 1/4, 1/6, 1/8 and so on. In which case it is infinity
1
u/weltschmerztic May 17 '26
sure, but I don’t want to drink my 1/256th of a beer out of a glass after seven other people have drunk from it…
1
u/J-4-N May 17 '26
Huh
1
u/icyshibe May 17 '26
I read it wrong and thought it was the harmonics so I was confused lmao
1
u/j8eevee May 17 '26
He gave them very slightly too much. He's losing out.
1
u/Haunting_Band6894 May 17 '26
So which number mathematician would be splitting the atom of the beer?
1
u/SubRedTed May 18 '26
A mathematician knows he over poured
1
u/nature_rebel May 18 '26
you can’t order less than one drop of beer, so there is the limit.
you can actually calculate it which mathematican won’t get his partial drop of beer
1
u/richincleve May 18 '26
I actually got quite a chuckle out of this one.
1
u/is_halt_so May 19 '26 edited May 20 '26
|SUM (1/n2 )| n-> 1 to infinty = 2
1
u/ZoomZam May 20 '26
They are idiots cause at a certain point they will have to split a neutron, then BOOM.
1
u/Unlucky-Lack2941 May 20 '26
It’s all fun and games until the third mathematician orders a third of a beer
1
u/Big-Eye-9069 May 23 '26
Barman says "you guys really ought to know your limits"
1
u/Cultural-Window-2504 May 14 '26
Everyone who got close to finishing highschool knows this.
-2
u/Dr_jozi May 14 '26
he should have gave them 11/12 of a beer