An infinite number of $1 bills and an infinite number of $20 bills would be worth the same
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- Опубліковано 30 жов 2022
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An infinite number of mathematicians walk into a bar. First orders a beer, second orders half a beer, third orders a quarter. Bartender pours two beers and says, "y'all should really know your limit"
Second order half a beer, third orders a third - bartender pours infinite beers.
@@MrCmon113 the first orders one beer, the second orders four, the third orders 9. The bartender pours 0 beers
@@xchomphk.9788 the first orders one, the second orders one, the third orders one. The bartender pours -0.5 beers.
The first orders one, the second orders two, the third orders three... So the bartender pours -1/12 beers
The first orders n1, the second orders n2, the third orders n3, the bartender pours x.
Mad props to whoever built the table capable of holding two infinite stacks of bills.
The piles are so heavy they have their own gravity and the top pulls on the bottom
Yeah weirdly enough the infinite stack of bills has a finite force acting on it everywhere.
They are just paper, relax.
@@LuLu-ip4zb what top?
well but you have one on oneside and the other on the other side so it evens out like on a scale.
The hardest thing about having these two piles is actually laundering the money
An infinite amount of Skylar Whites (yo) running an infinite amount of car washes. Checkmate.
Why would you ever need to launder it? Buy out a bank and you're done... I heard Credit Suisse would've let you buy them at a discount... Think of the savings!!! 🤣
Oh the irony...
@@alexjenkins8026You'd inflate the economy tho
We'll need a bigger washing machine
The biggest problem here is not that people don't remember details, it's that they will still confidently state something based on the thing they don't even remember.
They all remembered "sone infinities are bigger than others" but forgot, or maybe never understood, what that means
@@SheepHairOGno, they heard it, understood what it meant, forgot everything except for the phrase, and co-opted a great learning moment into a shortcut to make their tiny brain “understand” how infinity works easier. Because thats why these people say this. Its the easy way out, to not have to deal with something as complex and sometimes scary as infinity
Or people are just forgetful, especially when it comes to something they don't use in their day-to-day life.
Dunning kreuger
@@metaslavegaming9075 Yeah, I guess this is a good example of that. They learned a bit, assume they're an expert since the video was well-explained, but forgot the contents itself.
Hi Matt, I'm a bit confused. When you stand up and walk towards the door I can see the top of the infinite stacks of bills. Since you tower over them, does that mean that you are infinitely tall?
Lolol
Yes. But as you can also see both stacks have the same infinite height. Easy way to settle the argument.
Matt on the other hand is a different type of infinity.
I am impressed by his infinitely strong desk holding 2 stacks of infinite weight and a laptop and then ..
26 infinite stacks
@@RobBCactive I think you're thinking too small. Those stacks have infinite mass, and should suck in the moon, the other planets, the Sun, and just keep right on going, pulling in the galaxy and eventually the entire universe... or maybe instantly. I don't actually know how infinite mass works.
Though, I suspect it would draw in everything at the speed of light, since things can't move any faster than that. It requires infinite energy to move things at the speed of light, but seeing as we have that...
Additionally, that energy contributes to the mass of the objects, so they'd all have infinite mass as well.
What is this, Zeno's Paradox part two
"Infinity is not a process where you count and count and count and count and you eventually get there, it's a process of looking at all of it at the same time." is the best explanation of why infinity doesn't work like it feels like it should that I have heard in 38 years.
No, infinity is not a process. It's simply a number larger than any finite number. Also note that the word "infinity" itself is ambiguous on what "number" it belongs to. It may be infinity of cardinal numbers (which is still ambiguous about which one), ordinal numbers, surreal numbers, extended reals, or something.
Also "some infinities are bigger than others" is true in cardinal numbers but false in extended reals
@@xwtek3505try again, that didn't make much sense
Infinity is not a number. If it was, why are you not allowed to divide by 0?
@@LyuboRyuk It's not a *real* number. The statement "infinity is/isn't a number" is ambiguous and might possibly be false depending what set do you call a "number".
You can't divide by zero on a real number, because it would violate the division ring axioms. You *can* divide by zero on a projectively extended real number, and the result of a/0 is unsigned infinity if a isn't also unsigned infinity.
Wait, I thought the whole idea of comparing infinities was the one to one mapping. So if you can map every $1 bill to every $20 bill, is it not worth 20x?
An infinite number of days is as long as infinite number of hours.
But I would still pick the twenties, since they're are more convenient to use (which matters becouse I will be able to spend only a finite amount)
Does that mean an infinite amount of horses isn’t larger than an infinite amount of cats? Because I heard that cats and horses are actually the same size, but cats just stand farther away
@@YeaaIJusShiddedOnEm yes, even if each horse is 100 times bigger than each cat, the size of infinite amount of horses will be the same as the size of the infinite amount of cats. But it's only true if we are talking about the same kinds of infinities.
Becouse if you have as many cats as there are irrational numbers and as many horses as there are rational/integer/natural number, than for each horse you have there is an infinite amount of cats (but the opposite isn't true), in which case you have way more cats than horses (infinitely so).
But if you cut each of the infinite number of cats into infinitely small pieces and counted each fraction of cat, would it be more massive than an infinite amount of whole horses?
As someone who makes tips, I can confirm that having $100 in $1 bills is quite annoying.
@@spencercase5370 infinity times constant is still infinity so nah.
Reminds me of the time I had like $82 in singles to use up, so I brought it when I was hanging out with friend. One of them asked why I had so many singles, and for some reason my brain saw fit to say "I was at the strip club last night, but I think I did it wrong."
Nah, you did it right... LOL!
I respect the editor for spending all that time rotoscoping those piles.
It’s their attention to detail why I keep them employed.
@@standupmaths do you let them out the editing basement for five minutes a day at least?
Alex Genn-Bash puttin' in the hours
@@superkobster Not for five minutes. For π minutes.
@@professorx3060 τ minutes, when he is generous
There's a really weird visual glitch around 9:53 where the two infinite piles of money look like they're only finitely tall for some reason. I'm not sure what could have caused that.
Perhaps an infinite portion of the notes is also infinitely thin...
One could say it's a Parker animation, I suppose? At this point I think Matt has embraced it lol
UA-cam compression error...
They didn't want the piles to cover Matt as he stood up, so they just took a portion of each pile and stacked it on top. No bills were really removed.
The piles are actually infinitely high, however, special effects were used to make it appear as though the piles were not, for the comedic value. Matt has a highly skilled post production team.
To be fair, this entire video could just be "an infinite number of bills leads to infinite inflation which leads to all the bills being worth nothing", but the math angle is great as always!
And also the infinite number of bills would drown us all out anyway.
An infinite number of bills collapsing the earth into a black hole would be your most immediate problem.
only if you would actually spend it
@@Ruok90unless they are spread out from the earth
each individual bill may be worth nothing but the stack will actually just be worth all the money. owning the infinite pile would simply mean, that you own almost all the money.
I feel bad for the guy in the infinite hotel that was in room 9.2730173793729028373929263*10^104 when they had to move to double their room.
Umm the first coefficient in scientific notation can’t be 10 or above 🤓
@@AgentI0Ii never made that mistake, you're imagining things
Dubbel is not the word you are looking for
I'd still take the 20s, since they're easier to buy stuff with. Hopefully it includes an infinite bag of holding.
But what happens if you try to grab a bill and you accidentally make the stack fall over-
@@shablam0 I wouldn't take either of them as they probably are black holes
unless you are planning buying country yearly worth of production of whatever. What difference does it make?
@@ricardomiles2957 time management and space on hand.
Say you go to the store and buy $100 dollars worth of groceries. You need only have 5 $20 bills and that’s easy to pull out and hand over. 100 $1 bills is much more time consuming to count out to make sure you have the right amount and hand over.
Also with the $20 dollar deal, you can easily pay for most things by just handed over a few bills and you can get change for what you over pay to give to others. You can’t easily make transactions if you only use $1 bills especially as the cost goes up.
$100 purchase = 100 $1 & 5 $20
$500 purchase = 500 $1 & 25 $20
Dealing with $20 bills over $1 is much more convenient
@@crow2989 you get a limitless credit and only touch your money once a month. Here, way more convenient and still doesn't matter
The problem with the Hilbert Hotel is that to get a room at short notice you may have to bribe an infinite number of desk clerks - and you better have an infinite stack of $20s because there's no way these guys are gonna be happy with singles.
make sure to bribe them all simultaneously tho! or its not on very short notice anymore.
@@syro33 Ha! Good point, Syro! 🤨
My problem would be that I always had to move rooms just because someone comes or goes
Yes but you can give each of the infinite clerks 100 bills of $1 and still have dollars to spare
@@tomlxyz We could find a pairing where you have 0 probability of changing rooms, eg all current guests in a room that is a perfect square go to the room that is four times their current number, and the kth arrival goes to room (2k+1)^2. That way, the lim to infty of proportion of guests having to change goes to 0, so there is 0 probability you would have to change rooms but we still could accommodate all guests.
the solution to this problem can be simplified to “infinity times 20 is still infinity, stop trying to shove an unrelated concept that you don’t fully remember into this situation”
prove it tough guy
You can’t do calculations with infinity so that’s wrong
@@AgentI0I**sighs** the limit as x approachs infinity of 20x is infinity; satisfied? Besides, whoever told you you can't calculate with infinity was either oversimplifying or didn't know what they were talking about, you can totally calculate with infinity as though it were a number, you'll just have to accept that stuff like subtraction and multiplication between two numbers won't always be defined (the relevant search query here is "The Extended Real Number System")
"Nope. They both equal infinity in number. You just have way more single bills than 20 bills."
liz-pls, my dear, you are giving me a stroke
Think of it as density, way easier to comprehend
... we understand what the sentence is trying to say, it's just wrong
It depends on how you are defining the infinites, as not all infintes are the same size! Most people dont know this!
@@danquaylesitsspeltpotatoe8307bro u just said what he spent the entire vid talking abt and still got it wrong
@@drcraby356 Please tell me what I got wrong? Clearly your lack of knowledge means you cant define the three types of infinite! or even their names! 🤦♂🤣
When I teach about infinity, I like to point out that most mathematicians don't use "infinity" as a noun very often. They say that sets are infinite, or that a set contains infinitely many elements (adjective and adverb) instead. When they do say "infinity", it can usually be easily rephrased without the use of that word: "This quantity increases to infinity" means "This quantity increases without any upper bound."
Yeah. There's "the limit as n approaches infinity", but again that's "approaches", not "equals".
What’s a situation where they would use it as a noun?
In physics we always specify uncountable or countable infinity which keeps you thinking of it as a thing rather than a number
@@ericsilver9401 Potentially if they're working with the extended reals or the one-point compactification of the reals, one might refer to the point at infinity as just "infinity". But that's basically just taking the real numbers and adding an extra number in (or two in the affine case, one positive and one negative) that you call infinity.
I can't really think of any other case where it's not just the mathematician being lazy and/or sloppy (which does happen). In calc/limit applications, it really should be read as "approaches infinity" or similar, and in set theoretic versions of infinity, it really should be a more specific value (Like aleph-null, which is the smallest infinite cardinal) instead of infinity.
It's the difference between potential infinities and actual infinities. That's also the reason that actual infinities are impossible in reality.
The whole time I was worried about Matt's safety, if he had knocked over one of the stacks, he would have been buried in an infinite pile of bank notes 😲😵💀
I think that the pile would destabilise enough to spontaneously create a black hole or an infinite number of black holes in a line and he'd be stretched after he was squished, but also only after a very long time depending on the viewpoint
@@blumoogle2901 oh no! poor Matt 😧
:o
Which one is heavier though?
@@blumoogle2901 Infinite amount also means infinite distance, an as we know gravity is weaker with more distance.
All those people misunderstood Vsauce's video.
Something interesting I think is that if you take the set of all infinities, it’s an infinite set, yet, it is just as infinite as all of its infinitely many components.
But is it a set that contains itself...
The set of all infinities isnt an infinity im guessing
@@julianrobertson1869 it is not a set it is a class it is ABSOLUTE INFINITY
@@theblinkingbrownie4654 Depending on what you mean by infinity, it kind of is. There are two possible things that are being referred to. Neither of them are sets. There is Ord, which isnthe proper class of ordinals. These are infinite numbers that have an order to them and you can do nice arithmetic like adding 1 to them and they actually get bigger. Contrast this to the other notion of infinities, the proper class Card. Cardinals are kind of like unordered infinities, where the only way of comparing them is by their size. The size of cardinals is a more absolute notion, whereas the size of ordinal cares about the internal structure of the ordinals themselves. The statement that x is an ordinal is called Ord,and similarly for Card. These are not sets, I.e. there is no sets which contains ever x satisfying the statement of Ord or Card, but they still make sense as mathematical objects.
What's funny about people quoting Vsauce to justify their wrong answer is that Vsauce also says the line "There are as many even numbers as natural numbers" and then immediately proves it
VSauce is for high people to watch as long as they're not sober enough to catch the errors.
@@tristanridley1601 errors?
@@tristanridley1601 never gotten high, but i find many of vsauces math videos as helpful ways to visualize math concepts we can sometimes take as granted
@@tristanridley1601 What Errors?
Everyone who replied definitely watched the Vsauce video like 3 years ago and only remembered the part where there are different types of infinites.
If a number said "I can't even" then it's definitely an odd number
The last number is odd confirmed.
There's multiple layers to this joke :-O
That's odd...
Brilliant
That's an odd joke....
This should be mandatory viewing before starting to learn about series and limits in calc2 or whenever. I had an amazing instructor who spent a whole lecture going over why we have to be so careful when applying infinity as a tool, but I know most people aren't so lucky to have passionate instructors who want their students to love the subject! We need more people like you and Grey and Grant and pretty Derek and Michael and Steve in this world!
The comments have real "1 kg of steel IS heavier than 1 kg of feathers." type of energy.
I mean, if you put a bag of feathers that truly weighs one kg, and weigh it on a scale, it's probably gonna display as weighing less than if you weighed a kg of steel because of the air and all
@IkkezzUsedEmber It'd be the other way around.
A slab of steel doesn't quite incorporate air very well in an immediate moment (not without oxidizing!), but a bag of 1kg feathers would inevitably have some extra mass due to the air nullifying the vacuum within the bag the moment you wanted to know if there's really 1kg of feathers in it.
Yup. Would be interesting to see 1 kg of vacuumed feathers compared to feathers in the open air.
@@guyman1570 Shouldn’t we take air pressure into account? The larger object will have a larger column of air pushing down on it.
I would add another measure of depth: An infinite amount of money is actually worth nothing, since it breaks down finite definition of worth that economics is based on.
If there was an infinite number of $1 bills and an infinite number of $20 bills, the dollar (as a currency) would be worthless. EDIT: I also suspect that there would be inconvenient gravitational effects.
You should say the value of dollar will reach 0. It would sound more mathematically.
Well, the Altarian Dollar _has_ recently collapsed ...
@@_r4x4 but a dollar will still be worth 1 dollar.
I don't know if gravity would actually be an issue, since the density isn't that great. But all of the universe would be filled which might cause other problems.
@@kj_H65f in nominal value yes, it would be worth 1$, but even 99!$ wouldn't be enough to buy anything.
Just want to point out how great the cut vfx is for the "room switching" shot where two Matt's come out two rooms, one leaves and one enters the second room. Really seamless compositing! Impressive!
This was a very enjoyable video to watch, and the part where you explained how there's an infinite number of squares (i.e. an infinite number of square roots) clicked in such a satisfying way.
I’ve always thought of infinity as a verb rather than a noun in order to save myself from problems like this. Especially in calculus, everyone wanted to treat infinity as a stopping point greater than every other number. I think it’s only human to think of infinity as a really big number because nobody can really fathom an infinite number of things, but if you picture it as the act of counting without ever stopping, it became easier to grasp, for me at least. So for this problem, rather than seeing infinity as a number and wanting to multiply it by one and twenty, you’d see it as a never ending supply of $1 or $20 bills.
You deserve more than an upvote!
Agreed. To me, that’s the only correct way to think of infinity.
All I got of that was the last part, which would have been my comment to the tumblr thread (or wherever this was posted)
If you have two infinite amounts of things with different values then the only difference is the value of those things, because you can never exhaust the supply of those things and will always be able to subtract from the infinite stacks or piles
I think it's a problem of perspective. We're comparing 2 sets of numbers against a different set of numbers, being the series of infinite 1's and 20's against the infinite series of all numbers. However, if you compare the infinite series of 1's to 20's then they are the same as a number set. However, if you compare them as a monetary amount at any point along the infinite number series then the 20's will be larger, that is to say comparing them as a monetary amount that can be viewed and compared at any specific point in a series, not the series itself, which I think is an interesting way of looking at the setting.
Though we're talking worth... if it's based on value whether it's an infinity of $1 bills or $20 bills, it has infinite inflation and both become worthless. Any currency with infinite amounts is garbage as a currency because the value of each bill is "approaching zero" in worth. The $20 pile would inflate faster while being as worthless.
It was never a maths problem of units. The original post may not have meant it this way but it's true from this angle.
when people are taught infinity they really need to be taught that it is a concept not a value
eh depends who you ask
@@tobyconner5827 no, infinity is the concept of a sequence that doesn't end.
@@ComfyCherry infinitY is a concept yes but different infinite numbers exist and they are comparable to each other numerically
@@tobyconner5827 no, countable and uncountable infinity are not the same as “having different numerical values” dumbass
@@burtdanams4426 in what way
what i mean by numerically comparable is simply that they have different sizes
Great editing! The shots of the money canon and the hilbert hotel are really entertaining and well set up.
people starting a totally incorrect statement with "WRONG" is tough to read
9:50 I love the comedy of this zooming out part and showing that the stacks are, in fact, not infinite lol
I somehow didn't even pick up on this
it wouldve also been funny if instead of showing they're finite, they continue to go beyond the frame of the camera when it pulls back
@@MixMastaCopyCat but imagine if the editors scrambled to edit in the missing money post-editing after it zooms out
@@potats5916 what. wdym?
Actually they are infinite. Above the ones you see there's just an infinite number of these bills that are also infinitely thin...
Matt: "I couldn't get my hands on US dollars"
Also Matt: **shooting $100's from the money guns**
No no no, see he couldn't get the literal DollaDolla Bills, yo, so it's all about the Benjamin's baby!
@@dustysparks Well I certainly _hope_ it’s not somehow about my baby!
He meant he couldn't get his hands on an infinite pile of US dollars.
@@JavSusLar Fair point. After all, he _did_ have infinite piles of £20 and €500 notes
Those are WE dollars comrade!
Always good to watch a new continuum hypothesis video. I would have started the first example with 25 notes corresponding to the next note on the other pile and showing a one to one correspondence, but the way you began was equivalent. I would just argue it’s easier to visualize 25 note chunks lining up but that’s just an opinion. Well done
An infinite number of mathematicians walk into a bar, the first orders one beer , the second orders 2 beers, the third orders 3 beers and so on.
The bartender laughs and pours -1/12 beers.
There's another version of the joke in these comments where the first orders 1 beer, the second 1/2 beer, the third 1/3 beer and so on... The Barkeeper just puts two glasses in front of them and says: "You guys really should know your limit"
@@TheHimbeerjoghurt that’s probably a better version tbf
I tried to make a stack of infinite $1 bills and another of infinite $20 bills but I only had 5 of each. So to round them off I just wrote "IOU infinite $1" and "IOU infinite $20" on two pieces of paper and put them next to each pile. Thing is, my pathetic stacks of bills looked, well, pathetic, so I took the $1s and $5s back, just leaving the two pieces of paper. After all, it amounts to the same, right?
Thing is, now I feel like I gained $30 somehow, so I bought a big bucket of fried chicken. Win, win, I feel.
This is a story of hope and triumph in the face of mathematical confusion, and exactly what the world needs to hear right now
You, Garrick, are a visionary and a genius. I need some fried chicken now.
You’re my hero
The fact that the maths and the denominations don’t line up just makes the joke even better. Hope you’re still enjoying the chicken ☺️
best comment ever
Matt definitely needs to make a video showing us how he put the infinitely large stack of money into the finite space inside the money gun.
They're bigger on the inside.
Just define their thickness as one 1/2^n times the space in the gun
probably just a hole in spacetime
You just put 1 bill in the first half of the machine and the second note in the half of what's left and so continue, and that's gonna take an infinite amount of time with so much unused space left, unless, of course, you want to be finished by midnight, then you just watch the video again: and the answer will appear. I think he calls it Math-a-magic ❤
Immersive portals mod intensifies
The looking at the watch waiting to finish infinity shooting money end made me smile.
This was a fantastic video on infinities. It's a great explainer for how infinity works, and why it's just not straightforward to understand.
They're both the same, because if you look closely you can see that both stacks adds to a single -1/12 dollar bill.
Numberphile still hasn’t apologized for that bogus video
@@GAHAHAHH You're totally right.
@@MikehMike01 what video
1+2+3+4... there is no subtract, there fore it cannot be negative.
so thats kinda dum
@@kidredglow2060and yet it does...
An interesting thing about the Hilbert Hotel is that, if you want to add an additional infinite number of people, your guests had better be OK with traveling arbitrarily large distances within the hotel to get to their new rooms. I feel sorry for the guest in room #1,000,000, who has to walk a million rooms down the hall to get to their new room, and it only gets worse from there.
Depends on the geometry of the hotel
The same guy walked a million seats to get to his seat in the bus, I'm sure he'll be fine
If it’s a hotel built within infinite dimensions then no guest actually “moves”.
@@boggisthecat Would you please elaborate on this?
@@SappinYourSentries: You currently exist in three-dimensional space. Assuming there are an infinite number of points between your top and bottom and your left and right, then there are an infinite number of two-dimensional planes that you're currently occupying. That means you've arrived at all of those two-dimensional planes simultaneously (all infinity of them).
As you scale up the number of dimensions, the idea is the same. The way you in a three-dimensional space interact with two-dimensional spaces is similar to how someone in a four-dimensional space would interact with three-dimensional spaces.
An argument could be made that there aren't necessarily infinite physical points between any two points, but that doesn't matter here anyways, because Boggisthecat said "infinite dimensions". In an infinite-dimensional space, it would be arbitrary to not only allow someone to stand in front of an infinite number of doors simultaneously, but to allow an infinite number of people to do the same thing at the same time.
You are a hero for linking Limmy’s show
Second time watching this video, and I simply loved it just as much as the first time. It's just such a pleasantly brain busting subject, I think it perfectly matches how I'm feeling in finals week.
Had the pleasure of meeting Matt at a charity do once. He was surprisingly down to earth, and VERY funny.
I don't know if it is surprising. He seems like a friendly bloke on every account.
@@knutthompson7879 It's a Limmy quote.
@@danielchiverton4168 Ah, pardon my ignorance.
@@knutthompson7879 It's a limmy joke that he puts up whenever someone has died lol or whenever he's faking a death 🤣
@@i.m.crazee5195 Got it.
I can't believe you actually had someone read the whole hyperlink out loud 😂😂😂
I love that you explained this without using the term "bijection"
Ugh, I remember in engineering in university being introduced to the delta function that approaches infinity at one discrete location and is zero everywhere else. If you differentiate it, you get the unit step function. If you integrate it, you get one. It can be multiplied by real numbers. So, it is like a box with infinite height and 0 width whose area is 1, and you can multiply infinity by real numbers and have some infinities be bigger than other infinities. It’s trippy, because what “it is like” helps you understand it but it is not mathematically a thing and can really trip you up if you treat it as if it is. Infinity is so neat. You just have to keep reminding yourself crucially that infinity is not a number.
"20 gets to infinity faster" really puts to show the kind of thinking that comes up when you conceptualize infinity at The Biggest Number
Right? It's like no, they are infinite at the exact same time
Yeah, the 20s *increase* faster, but they reach infinity at the same time. Like lim x->inf of (20x+1)/(1+x)=20
@@tovekauppi1616 They never reach inifnity though, nothing ever does.
@@tovekauppi1616 They don't necessarily increase faster. When I make infinite piles of 1s and 20s, I always put thirty 1s for each 20
To me its just the idea of visualizing it as a function. 20x ist steeper than 1x, so if you use the same x, the 20x would reach any number faster. You dont have to think of it as the biggest number for that.
For me the confusing point is that math does seem to have chosen not to have any way do do a valid comparison here, while the "obvious" answer would be "compare one by one, no splitting/reorganizing of stacks", or "find the limit of both divided".
Similar to "what goes faster to infinity, x² or e^x?"
Is there really no way to quantify that density of whole numbers is bigger than just the positives, the evens or the divisible-by-42-s?
Each of those notes is worth 20 pounds? Wow, thats a really strong table. Stand-up Carpentry is what this has turned into.
The table is made from Infinitinium.
@@theuseraccountname The American spelling being Infinitum, though be careful not to buy the "Ad infinitum", once you buy one you can't stop getting more
Nice to see someone shouting out to Limmy, one of my favourite comedian of all time
I seem to remember that he used to have segments on one of Charlie Brooker's programmes. I always used to mentally tune out during Limmy's segments, because I couldn't understand a word he was saying. I got the impression that we were supposed to discern something funny in them, but I could never for the life of me work out what.
The best part is I walked into this video thinking I knew exactly why those comments on that post were wrong, and thinking I knew where they got it from, and I was correct on both accounts. I love me some infinities, and I also love talking about infinities larger than infinity. But I never talk about bigger infinities without talking about reals. Good video.
Some infinite are bigger than other infinites but these two are the same infinites
5:40 Matt shooting money guns for so long he grows a beard was a nice touch. :D
Thank you for bringing this to my attention. I thought the gag was good but boy is it good. I need to pay closer attention
Spotted it, too. A muuuuch longer beard would have been nice. E.g. at the end of the vid.
Missed this, thanks!
I think Matt can actually grow his beard at will; it doesn't take long for him.
Matt's so smart i bet he filmed that first, then shaved
One day I was watching the video about infinite hotel rooms and I understood it quite well without having my brain falling to pieces. Since that day I haven't returned to the video again because i fear that i might not understand it this time.
I love your channel because it feels like Ian McKaye from Minor Threat/Fugazi is nerding to me about math, geometry, and physics.
I love how Matt also takes the role of an internet historian.
its accurate
This "you can't look at infinity as a process but at the whole set at the same time" really drove the point home to me, and cleared up some intuitive misconceptions that I had, even while knowing intellectually they were wrong.
Interestingly, this gets at the idea of the difference between a completed and a potential infinity.
A completed infinity is one which exists, such as the entirety of an infinite set. A potential infinity is one which is never reached, such as the end-point of an infinite iterative process.
To be fair there is some math where it really is more like a process and not about the end result, specifically limits.
Some of the ideas people have in these examples can be formalized as limits. If the pile of $1 bills like like f(n)=n, and the pile of $20 bills is like g(n)=20n, then the limit of g(n)/f(n) as n goes to infinity is 20. Or in the example with the ping pong balls, the end result might be 0 balls, but the limit of the process is infinity.
@@__nog642 Limits are basically how we fixed infinity. Calculus was more or less built on the principle of, if we just ignore the fact this doesn't make sense long enough, it kind of makes sense. With limits we are able to define situationally what we need. With this equation we want the value, and the limits of the values are both infinity. The limit of the ratio is 20 which is accurate but not the question being asked. Limits are a very interesting work around to dealing with infinity.
If it needed to be explained another way, the INSTANT you start considering the fact that youre counting, no matter the size of the number, you are now working with finite logic
@@piercexlr878 If you find it usfeul to think of calculus that way that's fine, but calculus is pretty rigorous. I don't think it's accurate to say it's just ignoring things that don't make sense. Also infinite cardinals make plenty of sense and are not calculus, calculus isn't the only way to make infinity make sense.
When I first started watching this channel years ago, I thought “Stand Up Maths” was a call to the quality and character of Math. But I’ve quickly come to realize, it’s a channel from a stand up comedian, who has a deep love for math.
it's a play on Mel Brooks's stand-up philosopher from History of the World, pt 1
i never realized that you contributed to vsauce's infinity video. i remember watching that video years ago and loving it.
I never expect to laugh out loud multiple times during a video about math, but Matt makes it happen. The image of him getting bored while shooting infinite bills out of a money gun is something I won't soon forget.
Especially because he hair grew longer between the cuts to it.
I tried to disagree, but...... I cannot.
Doesn't take much to make you lol, hey?
I’ve thought of it as mapping the set of nonnegative integers to each of the sets of infinite amounts of money(1 dollar bills and 20 dollar bills respectively). Effectively we’ve assigned indices to each dollar and can now have a common point from which to discuss the problem in terms of comparison at some position in both sets.
My jaw dropped when you explained that every number can be squared and tipped the balls out. Brilliant explanation on reframing how we look at infinity.
He tipped infinitely many balls onto the ground. How’s he going to clean that up?
This one presents a bit of a paradox in my mind. As he approaches infinity the number of balls in the box goes up. Like imagine at the 10^1000th ball how many balls would be in the box.. then magically when we get to 10^infinity we have no balls in the box.. it was doing nothing but increasing the whole time, but at the "end" of infinity we have none. I think it's kind of handwavy to talk about the end of infinity in a case like this imo.
@@akunog3665 I mean that’s sort of the point…
@@jcskyknight2222 I suppose. However, there are some infinities that do not have this paradox, so I pointed it out in this one.
For instance the geometric series 1+1/2+1/4+1/8+... does converge to 2, and it does so without paradox. As we add up more and more terms we get closer and closer to 2.. we don't explode, then at infinity collapse back as we do in the square number box problem.
@@SkyGravity137 to some extent this is true of any number. The number 2 only exists within the mind and mathematics.
15:00 - This is a great example and gets right at how even though we can talk about infinite quantities as "finished" things, there is no way to construct them. Your construction procedure is clearly broken - it's a perfectly valid process but it will never yield your final result. The "transient" never ends.
Mathematician Normal Wildberger has some very strong opinions on this front, which boil down to saying that we shouldn't really incorporate the notion of infinite quantities into mathematics at all we can't construct them. They aren't really "accessible.' Of course, the main reason we (think we) want them is not because of countable infinties - it's really the uncountable infinities of the real numbers that we consider vital to the foundations of mathematics. But Wildberger isn't a fan of the reals either - he believes we can build mathematics using only rational numbers. I'm not a mathematician, so I can't really venture an opinion on these "pure math" thing, but... I can't convince myself that Wildberger isn't right. I definitely think he's worth looking into, even if it winds up only being "exposure to the other side's argument" for you. I do think he puts forward extremely interesting "constructions" of things like calculus, for example, without reliance on the real number continuum.
All math is just a way of making the observable universe make sense.
Limited infinities that are bigger than another is just a concept to comprehend something inconceivable.
You're still logically confining something into a binary system we can digest easier.
We can't count up to an infinite number, because numbers are constrained and defined.
Technically speaking, ordinals do allow you to do arithmetic with "infinity" (or rather, with the natural number line itself acting as a number) albeit only addition and multiplication, not subtraction or division
here's another way to think about it: there are two magic bags which always give you the amount of money you ask of it. one gives you the money in 1s and the other gives you the money in 20s. since they always give you whatever amount you ask for, they have the same value and make their owners equally rich.
I thought of this too, this sidesteps the idea of having an infinite amount of something, which is not really possible
Well, until said bag floods the economy with bills and makes itself worthless for anything besides on-demand kindling.
Yknow, it might be even more valuable then. An unlimited natural resource. You could in theory produce enough bills to create a 2000’ tall mountain of bills. You could stop any pursuit, cross any gap.
@@HerpaDurpVg If you burn them that's infinite energy as well
@@Bob13454 fr, bringin back steam engines
A mathematician advertises a lottery where the prize is an infinite amount of money. A huge number of participants buy tickets, but it wasn't until after the winner was selected that the mathematician announced the mode of payment: "1 dollar this week, 1/2 dollar next week, 1/3 dollar the week after, ..."
You will get rich, just not anytime soon…
Isn’t that $2?
this be the same as the function (n + 1)/n, which still will converge to ∞, but just slowly
what you're thinking of is $1, then _half_ that next week, then _half_ that each week...
1 + 1/2 + 1/4 + 1/8 + . . . which will converge to 2
@@sirk603 i thought so too, then I did some research 😅 You Don’t Know Me has the right answer.
Psst. He has done one mistake, though ;) you don’t converge to infinity. That is the definition of divergence. But we all understand what he means. It is just a technicality.
@@youdontknowme5969 aaah that’s what I was thinking of, my Bad.
great delivery as always
Of all the clickbait titles you have the best .... so much so they aren't clickbait at the same time!
My first reaction when I saw this was "yes there's different size infinities, but these two are the same size, because they were constructed the same way" and I'm glad to get confirmation of that. Honestly felt pretty good about that since I learned this stuff around 25 years ago. I guess it stuck!
They’re both enumerable :)
Oh thank god, the comments on the thumbnail were making me second guess how i thought it worked. Not like im an expert on it but i thought i had an alright grasp
The 'size' of the infinities might be the same but the value is different. The value of the 20$ would be exactly 20 times the value of the 1$. The infinity is the representation of the number of bills, no their value. So if you graph 20x = y (represents 20$) and x = y (represents 1$) and you graph it out to infinity, the only spot it would intersect (meaning they are equal) would be 0. 0 =/= infinity
@@sirjdog21 They both have the same value, because as soon as someone figures out that you have an infinite number of anything, it becomes worthless. Both piles are worth a crashed economy and a long stay in prison for counterfeiting.
@@sirjdog21 I wonder what you are using to graph infinity...
If nothing else, this video taught me that not only is there such a thing as a money gun but even more so that someone saw it commercially viable to design, manufacture, and market them as a product to the point that at least two of them could be included in this video.
They seem to be common in rap videos.
I use mine at the strip club.
They're for strip clubs.
And other places, I guess, where being conspicuously reckless with your money is encouraged.
They are often bundled with the dollar glasses...
Damn good editing. 10/10
There's something magical about someone stealing a post from reddit, it getting passed around, and then someone misattributing it to the person who stole it and then saying it eventually got posted to reddit that's very magical. Hope you do more due diligence in the future when crediting things.
“From my point of view they touch” is such an underrated throwaway line in there.
i think you might be projecting
@@abacussssss what?
@@abacussssss what?
Abacusss just learned a new word and tried to use it. So cute.
@@noahmay7708 Noah May just saw a comment and didn't educate himself on that the comment is a pun before commenting, how cute.
He even let his facial hair grow to show that he would be bored with the money gun.
Great attention to detail!
Oooorrrrr that was the first shot and he merely shaved to show the beginning sequence
@@joshl90 Yeah that makes more sense, good thinking :P
@@joshl90 it's still attention to detail
@@leadnitrate2194 I agree that it’s great attention to detail.
I love Limmy. Such a good comedian.
Lol the narrated youtube link is so good
I would just say, there is nothing you could buy with the stack of $500 notes that you couldn't buy with the stack of $20 notes, including a thing of infinite value. Both stacks could literally buy an infinite number of entire universes, and clearly neither stack could buy more than the other, since both would never be exhausted no matter how much of it you spent.
Succinctly put!
hmm, not convinced about the thing of infinite value. I mean, if you were to hand over the money bill by bill, then it would take an infinite length of time, which you haven't got. So I guess you would have to hand over the whole stack. In which case the smart move would be to pull some bills out of there before you hand it over and complete your purchase - but if you have a finite amount of time to pull out a finite number of bills, then you'd want them to be $500s and not $20s...
@@martinh972 But why would you pull out a finite number of bills when you can just hand over the entire pile and ask for half of it back as change
@@thedead073 I guess since you'd have to pay for the infinitely valuable thing by signing over ownership of the infinite stack of money (rather than handing it over, since it would have infinite mass and would take an infinite amount of time to do), you would really only have to say 'you can have ownership of the infinite stack, except for an amount equal to [some finite number].' The finite number could be anything you were able to name, which limits you to the amount you were able to represent as a number. If you were naming physical notes I agree that $20 is definitely not the same as $500 notes, but if you were naming an amount of dollars, there would be no difference in value between what you obtained from either infinite pile.
Then you realize an infinite amount of something makes that something have nigh zero monetary value
I would rather choose the $20 bills since it’s easier to pay for everyday needs. Sure the $1 and $20 are both infinite but it’s gonna be a hassle to give out a bunch of ones to a purchase of around $100 if you ever do buy that amount. Plus, I would just give the leftover change from my $20 bill to donate to the store
You could just overpay, grab a random amount out and tell them to keep the change, that way you don't have to worry about having the exact bill
@@M0D776 buy a 300k car with 1 dolalr bills vs 20 dollar bills.
Thats a substantial difference.
Infinite amount of 20 have a higher utility therefore hugher value.
Also after a short while you would collapse the value of dollar and both piles would be worth next to nothing. As much as infinite source of paper you can burn to make electricity or something.
@@M0D776you could do the same with twenties, saves the other person time too.
@@HidekiShinichi It only depends on how fast you spend. Unless you spend like a million per day, economy would do fine enought. At least until you will get kidnapped or arrested and someone else would use that money.
Why bother counting, just give them a huge stack of $1 bills. It would make no difference to you if you'd pay $1 000 000 instead of $15.
Fascinating video! I wonder if you could cover the concept of dividing by zero? Or more specifically why in a practical space it makes sense, but mathematically doesn't.
To give a rough example, dividing is like slicing up a pie, cut a whole intona number of pieces and you're left with that portion. But if you cut a pie into zero pieces, then there is no pie, and no portion, the result is zero.
However in maths, that doesnt work that way, and id like to hear you talk about why and how that is
I would like to mention, that you did not mention negative infinity, which is kind of cool to know that there are 'two' infinities.
the quality of the post production in these videos is great.
M. Parker should be proud of his editor Matt P.
It's clearly a Parker edit
As someone who's studied economics, I have to add something to the first meme. Due to inflation, they would both be worth nothing, and therefore, the same!
You receive infinite amount of money, but you must declare the income, and pay 10% taxes on that infinite amount, which is also infinity. So you have no money left, but you are the biggest taxpayer ever and the government spends 10k to make a monument of you.
@@doomdrake123 You'd still have infinite money since 10% of infinity is still infinity
@@williamdrum9899 I think you missed the point of the video…
@@williamdrum9899 if you had to pay 10% of your infinite dollars to the state you would end up with $0.
you add 10 ping pong balls numbered 1-10 to a box, and then take out the ball worth 10% of the highest number, which is 1. half an hour later you repeat this but with balls numbered 11-20. then you remove the 2. you do it again with the next numbers 15 minutes later. and so on and so on.
an hour has passed since you started and the box is now empty. even though on each turn you added balls, every number can be multiplied by 10 therefore every number will get removed.
@@emporioalnino4670 alternatively, you could add 9 bills to your box and put another bill in the tax box, instead of adding 10 and removing 1, and by the end you'd have infinite money in both piles, with every tenth bill in the tax box and every other bill in your box. these are two different processes that will leave you with different amounts of money by the end.
The shot of 2 Matts changing rooms in the infinite hotel. The Matt to the left catches the door that the Matt to the right opened. Love Matt's little vfx magic tricks in these vidoes. That took significant effort and adds nothing to the math explanation. I love it
I'm wondering how it was done, seems so seemless apart from the inverted doors
Aleph-0 describes the entire amount of numbers there are. It also describes the amount of odd numbers there are, even numbers there are. All the fractions that exist. And all of these categories are the same size, even though there is an infinite number of fraction in between two whole numbers.
Can we get Captain Disillusion to figure out how Matt's editors put the money piles there? I just don't get it, they look way too realistic for them to be just "edited in"
CD already covered this- he literally says the technique in the video. rotoscoping, cloning, blending, probably some… 3d…. some visual… effects. use your brain.
Clearly there were more infinite money piles in the back room. All practical effects, the talk of ‘editors’ was a distracrion
Umm what
I'm so happy I came across some fellow CD fans in the wild. That being said, the money piles were real. They were trained specifically to star in films, although they were cloned in editing, since there isn't an infinite amount of trained money actors
@@barryb.benson7572this is all wrong!money only does that when it's in a stressful environment!!!
I think I know what Matt is gonna do with these infinitely big piles of cash. He still has to pay for renting the infinite hotel for filming
good thing he will still have an infinite amount left over.
Universe could not contain an infinite amount of dollar bills.
I dont know if my way of thinking really "works" but this is how i wrap my head around infinity. If i had infinite amount of something it would never end. If my car had infinite gas, id never have to refill it. If my phone had infinite battery life, i wouldnt have to charge it.
So if i had intinite number of any bills, no matter what each bill was worth, id never run out of money....
you take the stack of 1's, i'll be taking the 20's
Can I just express my appreciation for the amount of work that likely went into that visual effect at 10:43 in particular (along with all the rest, of course) and getting it flawless. Amazing!
3:43 was also particularly impressive
Definitely! Most people understand the basic split-screen duplicating visual effect, but this case was that slight bit more interesting and advanced to the point where I had to do a double take. Bravo to the editing team!
...And to Matt for the video, of course. It was nice to slightly clear up my understanding of infinity.
it was so good i didnt notice it
Matt and Limmy is the most glorious cross-over I never knew I needed
Limmy?
@@louisBrother1988 guy in the thumbnail is pretty famous comedian in the UK
@@louisBrother1988 did you watch the video?
Very fun, entertaining and inciteful video! Personally though I would have just argued that the original statement is false. To create a stack of bills they all have to exist at the same time and there must be a finite quantity existing in the stacks. If it was phrased that the stacks would be added to perpetually over time then the question may have been which would be worth the most in the end, but that would introduce a new finite point where the bills could be counted. If the amounts were truly infinite there would be no point at which either amount could be counted and judged against each other, so to say they are the same amount when they are actually infinite is false.
I visualize it by thinking of a twenty as 20 ones. So you would have to insert 19 more ones between each original one to match the 20s side.
What I love about this topic is that it is so counterintuitive, but if you are careful it's actually not hard for people to follow. As a teaching assistant, one of my roles was to take groups of ten-year-olds at our local school who were bored by the regular maths lessons and do stuff to keep them engaged. One session we looked at how you could build different types of number from a few simple rules (starting with 1 and + to build the counting numbers) and discussed closure, next time we moved on to the concept of infinities. I worked through Hilbert's Hotel with them, but we had some time left so I decided to have a go at talking them through proving that the set of reals wasn't countably infinite. I knew I was pushing it a bit, but they actually kept thinking well and made good suggestions for things to try, even though they didn't hit on anything that worked. Which was actually the whole point of the group - to engage with maths and exercise their thinking muscles. Unlike the regular SATs-orientated lessons, coming up with the "right" answer wasn't important.
Sadly I only did this once, in my last year there. I started out much more cautiously, but every group confounded my expectations so that I went further with the next. My lesson learned: never underestimate ten-year-olds.
I love this man. There's no judgment; there's no derision for not understanding math; there's just 100% explaining and teaching. And isn't that the essence of math and science itself? It's so refreshing to have that within our world of judgment and argument, which isn't to say that there isn't disagreement and arguing within the scientific community itself.
what about the comments from people read out with funny voices?
@@lgbtthefeministgamer4039 That's poking some fun at the arrogance of the people who posted those comments, not their lack of knowledge. We need less people who will overconfidently speak about things they don't understand, and more people who can say "I don't know" and ask honest questions.
@@etherealstars5766 I 100% agree with you
There is the reading of commenters in mocking voices.
I think when people say that theres an some infinities are bigger than others what they mean is something can be infinite in multiple dimension. Like an infinitely big plane is infinitely bigger than an infinitely long line.
The taxes on those infinite amount of bills must be insane
I love how wildly the production quality varies in these videos
It varies even throughout a single video!
I would say the production quality is consistently high, the amount of production used in any particular scene or 'bit' varies intentionally and with good effect. I love that :D
It's the bit where he walks from one hotelroom to the next one that did it for me. Still trying to figure out where the cut is 🤔
The real reason the two stacks are worth the same amount is due to the hyper inflation making each bill worth nothing
I'm not even sure this isn't just correct
@@thatchapthere I'm sure it is correct, I'm surprised not more people had pointed that out.
"There's an infinite amount of cash at the federal reserve"
_Dansa med oss, missa inte chansen! Nu är vi här med Carameldansen!_
That’s what I was thinking!
No, it wouldn't. The US printed a little over 2 trillion dollars last year. To extract that much money from a stack of $20 bills you would have to spend a bill about every 300 microseconds.
The US will contribute to inflation much more than you could with those stacks of money.
5:40 I appreciate the amount of prop work that went into this 10 second bit 😂
Interesting video! Though I feel the need to add that a lot of those tumblr comments saying "some infinities are bigger than other infinities" are probably quoting the romance novel The Fault in Our Stars by John Green. He's been a huge meme on that site for years for... other reasons (if you know you know, and if you know i am very sorry).
I love how people in the comments instantly become confused again of the concept of infinity after Matt tried explaining it for 20 mins 😂😂😂😂