An infinite number of $1 bills and an infinite number of $20 bills would be worth the same
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Yes, I put in a second ball numbered 13. I'm going to claim that was on purpose. Spoooooky 13.
Let me know if you spot anything else!
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MATT PARKER: Stand-up Mathematician
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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.
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
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
@@BillyOrBobbyOrSomething 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.
"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.
@@waynestehle9114 Yes and no. That's one way to interpret the problem (but that means there is no fractions of dollars). That system is called cardinal number. But that's not the only way to interpret infinity. There is also calculus infinity that has nothing to do with cardinal infinity, for example.
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
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.
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!
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 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.
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.
All those people misunderstood Vsauce's video.
nah not all of them. many just forgot what they learned in the video, and they’re now unaware that they’re misremembering. quite sad tbh, but also very understandable-it’s probably something that has happened to most of us before
@@JohnWarosa999the brain can only hold so much information
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
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 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.
@@tristanridley1601 nah, watch the video it's good. The fault here is on people half-remembering 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.
@@TheZooBrooksAB don't be a debbie downer
Great editing! The shots of the money canon and the hilbert hotel are really entertaining and well set up.
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....
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!
This proves that there are a finite number people on the internet that aren't great at math.
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.
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.
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
@@lehk23 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.
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
@@BradlySmith-1932**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")
Why is it unrelated?
@@BradlySmith-1932i feel like I definitely remember using infinity in calculations when I was in calc 2 tho ?
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
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
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
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 can't believe you actually had someone read the whole hyperlink out loud 😂😂😂
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.
I love how Matt also takes the role of an internet historian.
its accurate
Funny how many people below still dont grasp it after such a well put together explanation, but at the same time it makes me worry.
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.
If there was an infinite number of $1 bills and an infinite number of $20 bills, the dollar (as a currency) would be worthless. EDIT: I also suspect that there would be inconvenient gravitational effects.
You should say the value of dollar will reach 0. It would sound more mathematically.
Well, the Altarian Dollar _has_ recently collapsed ...
@@_r4x4 but a dollar will still be worth 1 dollar.
I don't know if gravity would actually be an issue, since the density isn't that great. But all of the universe would be filled which might cause other problems.
@@20xx-mm-dd in nominal value yes, it would be worth 1$, but even 99!$ wouldn't be enough to buy anything.
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
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
@@TheHimbeerjoghurtthat's also wrong since that would add up to infinitely many beers. The actual joke is with 1+1/2+1/4+1/8 etc
@@eeromarttinen5372
Thank you for the correction. I thought that without the 1 it doesn't surpass the 2 but of course you're right.
@@eeromarttinen5372 nah, that's not wrong, since every next mathematician orders half of what the previous one ordered, so it's 1 - 0.5 - 0.25 - 0.125 and so on, total of which infinitely strives for 2
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.
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
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...
You are a hero for linking Limmy’s show
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
@@Lumens1 Yeah that makes more sense, good thinking :P
@@Lumens1 it's still attention to detail
@@leadnitrate2194 I agree that it’s great attention to detail.
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.
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
@@rondobrondo in what way
what i mean by numerically comparable is simply that they have different sizes
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
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
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.
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
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.
I don't think there was a single moment where I wasn't smiling while watching this video. You're so naturally pleasant to watch and unreasonably good at simplifying an explanation without dumbing it down!
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 🤔
Matt and Limmy is the most glorious cross-over I never knew I needed
Limmy?
@@JohnWarosa999 guy in the thumbnail is pretty famous comedian in the UK
@@JohnWarosa999 did you watch the video?
Thanks for making me understand infinity a little better! I feel that I had a pretty good grasp on the concept before, but now it's better!
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...
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.
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
Ah yes, "I watched a Vsause video 7 years ago and have forgotten everything about it except "some infinities are bigger than others"" Classic
“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.
"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?
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.
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.
Really excited to finally have LIMMY on the show.
The looking at everything at the same time and not sequential thing you said is the most concise way I think I’ve ever heard this concept summed up (pun very much intended). Next time my friends say “yo math geek explain infinity” I’ll be jumping right there!
Yeah, it's nice to finally have an answer since that question happens so frequently
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...
I only half remember this video, so I am watching again.
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.
That was a really smooth transition from room 1 to 2 that I don’t think enough people appreciate.
wow youre right, its looks so good i didnt even realise at first 🤯
Except for the very obvious bathroom sink where you should be seeing Matt's desk from room 1
not that one, the one at 10:44
I still can't tell how it is so smooth
@@exp5261 he catches the door his other self left open
This is such an incredibly accessible introduction to real analysis. Your skill in taking intimidating mathematics and then turning them into fun, general-audience-accessible videos is amazing.
I still remember to this day back in primary school some kid kept claiming that him and his brother just need two more pokemon cards to own "infinite" pokemon cards
Well, since "infinity" has been defined in this video as meaning "the entire set", they might have been technically correct.
I love these follow-up videos that correct the missconceptions people remember from previous ones.
I think these are often the breakthrough moment when this "fuzzy" knowledge that may warp and become wrong gets solidified into real understanding.
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.
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
That ping pong ball thing broke my brain. I'll go lie down.
You've got to respect Matt for his commitment here. Not only in acquiring two infinitely tall stacks of money, but also for cutting the logically implied holes into his ceiling to make space for them
I dunno, couldn’t he shave a bit off the top of the infinite stacks to pay to have his ceiling raised?
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.
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
@barryb.benson7572this is all wrong!money only does that when it's in a stressful environment!!!
After you go through the countable serial numbers, the Treasury is going to be upset about the infinite counterfeits.
I found this video immensely useful in giving me a better intuition about infinity. As a programmer, it's like the difference between declarative (every ball that has a square is not in the tank, therefore there are no balls) vs imperative (start at ball 1, then do 2, then 3 etc). Declarative works for infinities, imperative less so
It's also like a disjoint union, at midnight the tank consists exactly of the balls that were added to the tank without being removed later, and nothing more than those
I just wonder whether there is something I can put in so that 'float('inf') < x' that will evaluate as true (in Python)
Lazy evaluation supports non finite data structures
I love when Matt said “it’s Mathin time!” And then Mathed all over the place
Yeah now the inside of my screen is all covered in Maths... Math? Maths...
™️
I read that as meth
@@ninjabrawlstars7656 Jesse we need to cook!
Stand back, I'm starting to Math!
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.
Very cool of you to directly shout out the creator used for the reaction image in a meme, not many people would think to do that
Thanks for reading out the entire UA-cam link. That was really important to me
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.
"Iiii like your funny words, magic man."
Your ability to address a common misconception in such a engaging way is incredible. People like you make math less threatening and bridge the gap for the general public. I'm studying to become a high school math teacher and I wish to be able to teach math subjects as well as you :)
Just to clear up some possible misunderstanding of the last part: Based on our axioms, the question of what the next biggest infinity is makes sense (it’s called aleph 1). We can define a set which has precisely this size (using ordinal numbers, that’s what Vsauce talked about in the video mentioned). What we can’t show however is if the reals have the same size as this set.
I am currently preparing a presentation on the Continuum hypothesis so I had to nerd out a bit :D Awesome video by the way!
Thank you
Before this comment, I didn't understand what Matt's claim even meant. Now I feel like I understand what he was saying… I just don't understand how it could possibly be true
I'm not sure if you actually "cleared up" my confusion. You might actually have increased it. But I do feel better informed 😃
Reals have been shown using the normal set theory axioms to be larger than Aleph null. That's standard Hilbert Hotel paradox.
@@12jswilson that is wildly different from reals being aleph 1, buddy.
@@98danielray the reals have been demonstrated to be equal in size to the power set of the natural numbers, have they not?
@@12jswilson the power set is not the immediatelly following cardinality. they are just a strictly larger size. they could be the next one, not the next one or unprovably neither/either like it is with this case
Damn, glad to see Patreon doing infinitely well for you!
"∞/2 doesn't give you half of ∞, but instead gives you 2*∞, which is still equal to ∞" is my personal explanation on whenever people believe most fallacies on the concept of larger infinities.
I also love the irony in the fact that, in trying to determine how large different sizes of infinity are relative to each other, you _run out of maths_ before you're able to get an answer. 'Question too large, used up all the maths in the process of trying to answer it; we then attempted to ask a philosopher instead, but they kept answering our questions with other questions, so we gave up and went home. Would you like to see some slides we took of interesting marmalades at the tourist information booth on the drive over?'
This sounds like it could very well be a quote in the Hitchhiker's guide to the galaxy
Well for one thing set theorists and other metamathematicians like to play philosophers themselves, so really they asked themselves a lot of questions and then they all disagreed. :)
@@GeekProdigyGuy Yeah I was going to say, Matt is basically doing philosophy of mathematics in this video. To the point of almost saying "There are proofs of this in other (mathematics) videos, but as this is a philosophy video, here's the low-down about axioms."
limmy will watch this video on stream if you tell him he's in it. he LOVES being mentioned
great delivery as always
The commitment to reading those comments, including reading the web address, lol, love it.
The commitment on the address! Lol
I will never get bored of Matt's dedication to keeping a joke going long after everyone else would have given up with it.
Aitch tee tee pee colon...
forward slash forward slash...
double you double you double you dot..
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 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.
Can we all just appreciate the consistent use of brummie accents for reading out comments from confused posters!
I love how people in the comments instantly become confused again of the concept of infinity after Matt tried explaining it for 20 mins 😂😂😂😂
I met Limmy at a charity doo once. He was surprisingly down to earth and VERY funny.
Not enough people are laughing at this comment
He gave me my start in showbiz. My first gig: opening for him.
A good way we end up nailing down the axioms we all agree on is by deciding what actually matters.
For example, how the money pile ends up interacting with the world has sway over which pile would be preferred.
Can a pile be owned? If so, what does utilizing it look like?
If you merely have to point in the general direction of your stack of infinitely many bills to access its value, there’s no need for preference. Either way, you get the same value from the same generic action.
If you needed to take bills out to pay for things, then there would be a scale factor of 20x to the labor cost of retrieving the money for a purchase, which would, of course, lead to a preference, we being the finite, time-bound, utility maximizing wretches that we are.
Existential anyone?
What a man he is. All the infinite money and he is still making youtube videos
The "next biggest infinity" part at the end was a great little nugget, i've seen most of these ideas before but that one surprised me! Love your videos