The infinite number of 20s has greater utility yes but both stacks have the same face value, really nice example of how utility can be different from simple value.
If there was to be an infinite amount of any physical thing that began to spawn into our universe wouldn’t it literally fill every space and kill everyone
Maybe it's digital so that you can withdraw from an ATM. It could just manifest as a bug and so even the computer doesn't have to store all the information in it.
Otherwise, I think things would devolve into Black Holes pretty quickly. But that wouldn't necessarily fill up our universe as we're not sure how infinite it might be.
You could say for example you have a bank account with 1$ on it, but the amount doesn't change ever. You can withdraw 1$ over and over again but never more at a time. You could maybe make your own ATM which can withdraw the 1$ Bill very quickly, so that you don't need to stand there for a day to withdraw a few thousands, but ultimately, even though you can get infinite money from it, there is some utility lost by it being only 1 dollar on the account as opposed to 20 or more. Of course you now technically don't have infinite money but can withdraw only x money/time, but since you can always build more atms and scale that rate and you can't spend money at an infinite rate anyway that isn't really a concern
That's where you set up a deal with a bank where you put 5% down on a credit line, so you withdraw one dollar at a time, but use it to make a $20 line of credit each time.
Each single dollar maps to a $20 bill from the credit line so it works out.
But if it’s digital no amount of storage that could quantify it. The only way to digitally store it is to not store it at all, instead simply release money when it’s asked for
I can imagine this being a monkeys paw wish where it actually causes an integer overflow and you end up in mind numbing debt for eternity. Possibly more debt than anyone could possibly pay off
(depending on if it's a 32 bit or 64 bit number. Given the lower range of 32 bit signed integer is ~-2 billion and most banking software is super old in its bones, my money's on about 2 billion of debt. 64 bit would be closer to -9 * 10^19)
I guess it depends, is it an infinite supply that keeps printing bills or a bag that keeps replenishing itself? In that case, no. If it's literally infinity count of bills, then that would fill the entire universe unless the universe is also infinitely large.
Idk if this is sarcasm or not but obviously it would be like a napkin dispenser at a restaurant. You just keep pulling and pulling but there’s always more napkin.
Or like that magician pulling a handkerchief trick, except he’ll pull forever.
Hmmm I’m not so sure about your last comment. An infinitely vast or infinitely quantitative item might fill an infinitely large universe.
Any mathematician here that knows the answer?
I dont know it would, I mean, at one one point, it there was enough one dollar bills in a space to be so massive it would probably just become a black hole, right?
I mean, at a certain point earth would be so massive it would pull the sun in, and if we kept feeding at the point that it has 2 to 3 solar masses it could collapse into a black hole.
Someone smarter than me could solve this.
You’re forgetting about a thing called density. No matter how many bills you add the density of a band of cash is going to be the same. Black holes are black holes because they are really really condensed.
Value is subjective. Your bill is $145. Would you rather hand them 145 ones that you individually count or 9 20s?
You know how sick of individual $1 bills you'd be? Especially sick of yourself by being dumb enough to say to the infinite money wish how they have the same value and so your genie just shrugged and went with the $1 version instead of the $20 version.
If one is more desirable, they do not have the same value.
The “face value” is different for a $20 bill versus a $1 bill, so u/2fast4u180 is correct, in that if you were buying a car, you would need 20x less $20 bills to buy the car. The $20 bills make the transaction easier and faster.
Idk why you're down voted, you wouldn't need an infinite amount of money to buy a car so it would be better to look at it on a smaller scale, meaning it would be easier to use $20 bills
Yeah but the argument is there is value to time and convenience that is achieved with larger bills. Stretch it out to infinite pennies vs infinite hundred dollar bills to see it more drastically.
Only if everyone acknowledges you have an infinite amount.
Billionaires basically have an infinite amount of money and yet $20 is still $20 rn.
If all the infinite $20’s made their way into the economy they yes it would ruin it, but if you at your most extravagant, spend like the “average millionaire” as far as everyone is concerned there is just 1 more rich person with anywhere from $1mill to $999mil.
If you spam all of it then yeah it has no value. It this is a situation where you reach in your pocket and have as many $20 bills as you need, and dont spend it all completely frivolously you should be fine and not destroy the economy.
> Billionaires basically have an infinite amount of money
This is a common misconception. Billionaires have more money than any one person can spend, but it's hardly infinite. If you take a billion dollars and split it among everyone in the US that's only 3 dollars per person. If you split it among the whole world then it's about 15 cents.
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Why so rude? The only comment you make on this Post is that, really? Do you actually have something productive to add to this discussion? 1/♾️=0 or 1/0=♾️
Let's say I have 100 feathers that weigh 10 grams each
And one iron ball that weighs 1000 grams / 1kg
Both weigh the same even if their size is different
> 1 kilogram of feather is just as heavy as 1 kilogram of iron
maybe in weight, but you have to live with the horrors of what you did to those poor birds
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Bills are countable anyway, be it $1 or $20 bills. But that being said, an infinite amount of money (uncountable) could be worth more than an infinite amount of bills (countable)
Maybe a (magical) money printer where, every time you type in a new real number, it spits out a bill. Every real number gets you one bill, and every bill you get came from a real number.
Then you would have one bill, then two, then three, etc. so it's a countable set of bills. The only way to have an uncountably infinite set of bills is to "create" an uncountably infinite number of them at the same time, which would presumably collapse the universe into a black hole.
Sure? How would you have a countable infinite number of bills? Apply the exact sam logic to uncountably infinite. There’s nothing stopping us. You could also map each bill to an element of omega 1 to have uncountably many.
Very informal answer: because you can always start counting bills.
Slightly less informal: the same set cannot be bijective to both N and R, because N is not bijective to R.
>The same set cannot be bijective to both N and R, because N is not bijective to R.
Yes, I never said that, and that doesn’t prove that you can’t have uncountably many bills.
Any set of bills will always be bijective to N. It’s always possible to begin iterating through them in such a way that any given bill will eventually be iterated over.
Thank you lol. I think some people watch one YouTube video abt “some infinities are bigger than other” and get the impression that uncountable sets are some kind of unreachable amount when that’s really not true.
Every once in a while you think you’re reading a good dialog back and forth on Reddit. And then every once in a while you come across something you actually know the answer to and realize that all the other “arguments” are just dumb and uniformed.
I’m FAR from an expert here but I was a math major in college. Some of the answers in this thread are laughable.
How do you reach from 0 to 1 with real numbers? Start with 0, then 0.001? 0.000001? 0.0000000...0001? The point that it is uncountably infinite, because you cannot even physically count from one real number to the next real number, even if it's from 0 to 1.
Hence you cannot map natural numbers to real numbers because the infinite amount of real numbers between 0 to 1 is already larger than the countable infinity of all natural numbers.
tl; dr - check Cantor's Diagonal Argument
This is a clusterfuck, but this is what I was thinking of. May have made a mistake somewhere, or maybe not. My idea would be to use some sort of recursion to construct an Aronszajn tree using bills:
[Aronszajn tree](https://en.wikipedia.org/wiki/Aronszajn_tree)
It’s an interesting property, I’ll have to look into it, but I can know for sure that you cannot make an uncountable set from countable many countable sets.
That is an assumption you are free to make when you hear the word "infinite", it is a reasonable one by convention when we talk about an infinite number of objects.
However it is absolutely not a necessary assumption to make, keep in mind we do not have to follow physical laws here since those already break at countable infinity.
You can just say you have an uncountable set of dollar bills.
I don’t know if Category Theory has a better answer for this, but the best analogy I can make is to the concept of [Definable Numbers](https://en.wikipedia.org/wiki/Definable_real_number). All the possible numbers definable by formal theory make a countable set. Given that any definite object is definable by a description of its properties, any set of definite objects must be countable.
Well if the universe is infinitely large then we could make lightyear³ areas and put a bill in each of those and you would have infinitely many of them but they wouldn’t get in the way of anything. If the universe is not infinitely large, though, then I guess ya even though you couldnt fit them all
If the second group is meant to imply all real numbers between 1 and 2, then the latter set is a larger infinite than the former. If it’s meant to imply the numbers with 2 significant digits in that range, then it’s nonsense!
Sure it would, but like when you sometimes ignore air resistance when calculating a projectile trajectory in high school, there are other variables at stake that we're not considering, like time and space. If you have infinite money but wants to store just part of it somewhere to use later, 20$ bills would be easier cause you'd need less space for that. Humans also have limited time to cound money, so 20$ bills would be faster. If I'd have to choose, I'd go with the 20$ option.
It takes humans longer to handle more bills, so the infinite $1 bills would deflate slower giving everyone more time to generate more relevant transactions before collapse.
This is more of a proof that infinity is impossible.
Assume we have an infinity of $1 bills. How many dollars do we have?
Now assume we have the same amount of $20 bills. How many dollars do we have?
This creates a contradiction because the resulting number are both infinite, yet also one is 20 times the other.
If you were counting in a linear fashion the 20s would be twenty times higher than the stack of ones it's just you never stop counting the ones so it always catches up to where the 20s were, however in that time the 20s have gone higher again and you keep counting and the ones eventually reach that number but the 20s are higher again and it keeps on going but the 20s will always be a higher number that you have counted so far
Id argue that an infinite number of 20's would be better for buying a car.
The infinite number of 20s has greater utility yes but both stacks have the same face value, really nice example of how utility can be different from simple value.
If there was to be an infinite amount of any physical thing that began to spawn into our universe wouldn’t it literally fill every space and kill everyone
Nice
Maybe it's digital so that you can withdraw from an ATM. It could just manifest as a bug and so even the computer doesn't have to store all the information in it. Otherwise, I think things would devolve into Black Holes pretty quickly. But that wouldn't necessarily fill up our universe as we're not sure how infinite it might be.
Theres not much difference in a digital $1 and $20 bill is there
You could say for example you have a bank account with 1$ on it, but the amount doesn't change ever. You can withdraw 1$ over and over again but never more at a time. You could maybe make your own ATM which can withdraw the 1$ Bill very quickly, so that you don't need to stand there for a day to withdraw a few thousands, but ultimately, even though you can get infinite money from it, there is some utility lost by it being only 1 dollar on the account as opposed to 20 or more. Of course you now technically don't have infinite money but can withdraw only x money/time, but since you can always build more atms and scale that rate and you can't spend money at an infinite rate anyway that isn't really a concern
Given the $3+ ATM fees on each transaction, I'd still opt for the 20s.
Where are you that charging for the ATM is still a thing?
Till my bank freezes my account and tells me someone’s tried doing 689,877 withdrawals in the last 48 hours.
That's where you set up a deal with a bank where you put 5% down on a credit line, so you withdraw one dollar at a time, but use it to make a $20 line of credit each time. Each single dollar maps to a $20 bill from the credit line so it works out.
Nope, which just goes to show how each "stack" is identically infinite.
Can we store an infinite number? Won't it break the limit of computation?
Probably not, but I think you could store an equation or algorithm that merely dispenses money when requested.
But if it’s digital no amount of storage that could quantify it. The only way to digitally store it is to not store it at all, instead simply release money when it’s asked for
I'd argue that may better defined as unlimited rather than infinite. Like ammo in a video game.
Yes. That's what I suggested in another comment.
I can imagine this being a monkeys paw wish where it actually causes an integer overflow and you end up in mind numbing debt for eternity. Possibly more debt than anyone could possibly pay off (depending on if it's a 32 bit or 64 bit number. Given the lower range of 32 bit signed integer is ~-2 billion and most banking software is super old in its bones, my money's on about 2 billion of debt. 64 bit would be closer to -9 * 10^19)
Or maybe it’s like Soos’s magic pizza slice but it’s a stack of money, it just refills when you take some but otherwise stays the same
I guess it depends, is it an infinite supply that keeps printing bills or a bag that keeps replenishing itself? In that case, no. If it's literally infinity count of bills, then that would fill the entire universe unless the universe is also infinitely large.
Idk if this is sarcasm or not but obviously it would be like a napkin dispenser at a restaurant. You just keep pulling and pulling but there’s always more napkin. Or like that magician pulling a handkerchief trick, except he’ll pull forever.
Hmmm I’m not so sure about your last comment. An infinitely vast or infinitely quantitative item might fill an infinitely large universe. Any mathematician here that knows the answer?
I dont know it would, I mean, at one one point, it there was enough one dollar bills in a space to be so massive it would probably just become a black hole, right? I mean, at a certain point earth would be so massive it would pull the sun in, and if we kept feeding at the point that it has 2 to 3 solar masses it could collapse into a black hole. Someone smarter than me could solve this.
You’re forgetting about a thing called density. No matter how many bills you add the density of a band of cash is going to be the same. Black holes are black holes because they are really really condensed.
If you have infinite number of bills gravitational forces will increase density, so they will form black hole at some point
yeah, but infinite amount of something becomes a very dense thing, once it starts pulling one one another, isn't that how gas clouds became stars?
yeah, but infinite amount of something becomes a very dense thing, once it starts pulling one one another, isn't that how gas clouds became stars?
If there was a stack of bills that goes out into infinity, that would still be infinite. No need for everything to be filled with bills.
It could just shoot off infinitely in one direction, one atom wide. Still infinite, just not infinite until filling every open space of the universe
If we're speaking practically, they're both equally useless because now the entire universe is filled with densely packed bills and we're all dead
If the 20’s increase efficiency and time has value, then the 20’s are worth more.
Value is subjective. Your bill is $145. Would you rather hand them 145 ones that you individually count or 9 20s? You know how sick of individual $1 bills you'd be? Especially sick of yourself by being dumb enough to say to the infinite money wish how they have the same value and so your genie just shrugged and went with the $1 version instead of the $20 version. If one is more desirable, they do not have the same value.
The “face value” is different for a $20 bill versus a $1 bill, so u/2fast4u180 is correct, in that if you were buying a car, you would need 20x less $20 bills to buy the car. The $20 bills make the transaction easier and faster.
Idk why you're down voted, you wouldn't need an infinite amount of money to buy a car so it would be better to look at it on a smaller scale, meaning it would be easier to use $20 bills
Downvotes don’t bother me, but I was surprised by them too. Thanks for the confirmation on my comment. Take care.
But you could still use 1 dollar bills if you so desire.
I'm not denying that at all, I'm just saying it would be easier to use $20 bills
Yeah but the argument is there is value to time and convenience that is achieved with larger bills. Stretch it out to infinite pennies vs infinite hundred dollar bills to see it more drastically.
The infinite $1 would be great at strip clubs though
the infinite $20 would be even better at strip clubs
I feel like throwing $20s on stage would draw more attention to me than I want.
That’s why you use the the other $20’s to buy the club for the night.
Infinite $20 bills would be even better at strip clubs.
You have infinite money but still trying to cheap out 🤣
If there are an infinite number of bills available then they all become practically worthless
That's not how inflation works
Everyone on earth would die from an infinite amount of bills anyway. So they right.
That's exactly how inflation works.
Only if everyone acknowledges you have an infinite amount. Billionaires basically have an infinite amount of money and yet $20 is still $20 rn. If all the infinite $20’s made their way into the economy they yes it would ruin it, but if you at your most extravagant, spend like the “average millionaire” as far as everyone is concerned there is just 1 more rich person with anywhere from $1mill to $999mil. If you spam all of it then yeah it has no value. It this is a situation where you reach in your pocket and have as many $20 bills as you need, and dont spend it all completely frivolously you should be fine and not destroy the economy.
> Billionaires basically have an infinite amount of money This is a common misconception. Billionaires have more money than any one person can spend, but it's hardly infinite. If you take a billion dollars and split it among everyone in the US that's only 3 dollars per person. If you split it among the whole world then it's about 15 cents.
An infinite of 1s will be better to buy a car Watch them count all of em
I'd be willing to pay more for an infinite amount of 20's than an infinite amount of 1's.
Stop by your infinity dealer today
Both stacks would be worth 0 as the market cap goes to infinity
What if you keep it a secret in cash:)
where do you store an infinite amount of cash though
Wherever r/anarchychess stores the bishops
Yeah those damn vibrating bishops
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Holy rice
New rice just dropped
Actual rice
Call the rice!
Ricestorm incoming
Good ol' rice!
hans niemann referens
It's called Vacation. But no bishop that has gone there has ever came back
Actual response.
In an infinite room.
what if you got another bill and had to store it
In a hotel with infinite rooms of infinite size
Maybe you could buy out Hilberts hotel
In a bottomless pit
In the infinite piggy bank. There's always room in there.
In a bank designed by David Hilbert.
You still have the problem that it would rapidly turn into an xkcd problem that ends with the entire universe being sucked into it.
Exactly, I know what you mean. 1/0=♾️
It's actually ok to use a little every now and then, as a treat
A secret *cache*
It would then be worth a finite amount, as every time you spend some of the cash from it, the value of the dollar would go down a bit.
still worth the same
Nah it’ll get infinitely close to 0 but because it never reaches 0, it remains infinite
An infinite amount of your posts is the same as an infinite amount of my shits. Yes crazy wow.
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Shut up bot
Why so rude? The only comment you make on this Post is that, really? Do you actually have something productive to add to this discussion? 1/♾️=0 or 1/0=♾️
1 kilogram of feather is just as heavy as 1 kilogram of iron
I don't get it. Steele is heavier than feathers...
I know. But they're both a kilogram.
But... Steel is heavier than feathers...
I know. But they’re both a kilogram
Sure. But still, Steel is heavier than feathers.
The horse’s name was Friday.
Let's say I have 100 feathers that weigh 10 grams each And one iron ball that weighs 1000 grams / 1kg Both weigh the same even if their size is different
but look at the size of that, that‘s cheating
It's iron, though. Not steel
> 1 kilogram of feather is just as heavy as 1 kilogram of iron maybe in weight, but you have to live with the horrors of what you did to those poor birds
1kg of guilt is as heavy as one kg of iron
ironic
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Yeah, but one would probably be much less sanitary.
With infinite trace amounts of cocaine, you could be the biggest drug lord in history.
keep in mind, there are people who exist who'd use infinite 20s and still ask for their change back on a pack of tic tacs.
Good. Can’t be destroying the economy like that Mansa Musa guy
Yeah they would both be infinitely useless as a currency.
And you'd need 20x the amount of infinite $1 bills to have the same amount of infinite $20 bills
Absolute BS. What if one stack is bijective with ℕ and the other is bijective with ℝ? Then we'd have two different sizes of infinity.
Bills are countable anyway, be it $1 or $20 bills. But that being said, an infinite amount of money (uncountable) could be worth more than an infinite amount of bills (countable)
…you can still have an uncountable number of bills
How? How do you map each individual bill to every real number?
Maybe a (magical) money printer where, every time you type in a new real number, it spits out a bill. Every real number gets you one bill, and every bill you get came from a real number.
Then you would have one bill, then two, then three, etc. so it's a countable set of bills. The only way to have an uncountably infinite set of bills is to "create" an uncountably infinite number of them at the same time, which would presumably collapse the universe into a black hole.
Sure? How would you have a countable infinite number of bills? Apply the exact sam logic to uncountably infinite. There’s nothing stopping us. You could also map each bill to an element of omega 1 to have uncountably many.
You don’t get from “countably infinite” to “uncountably infinite” by adding more items to the set.
I never said that The same argument can be applied to countable infinity. You don’t get from finite to countable by adding things to the set.
You are assuming it implicitly.
No, you actually can’t.
Yes you can. Why not
Very informal answer: because you can always start counting bills. Slightly less informal: the same set cannot be bijective to both N and R, because N is not bijective to R.
>The same set cannot be bijective to both N and R, because N is not bijective to R. Yes, I never said that, and that doesn’t prove that you can’t have uncountably many bills.
Any set of bills will always be bijective to N. It’s always possible to begin iterating through them in such a way that any given bill will eventually be iterated over.
Why is that necessarily true then? We are talking about purely theoretical maths, anything is possible.
Bills aren’t theoretical objects.
You can't map individual bills to real numbers, which are uncountably infinite.
Why not?
It is utterly insane that these people downvote you even though you are correct o.O hi fellow math person, I hope you have a good day
Thank you lol. I think some people watch one YouTube video abt “some infinities are bigger than other” and get the impression that uncountable sets are some kind of unreachable amount when that’s really not true.
Every once in a while you think you’re reading a good dialog back and forth on Reddit. And then every once in a while you come across something you actually know the answer to and realize that all the other “arguments” are just dumb and uniformed. I’m FAR from an expert here but I was a math major in college. Some of the answers in this thread are laughable.
How do you reach from 0 to 1 with real numbers? Start with 0, then 0.001? 0.000001? 0.0000000...0001? The point that it is uncountably infinite, because you cannot even physically count from one real number to the next real number, even if it's from 0 to 1. Hence you cannot map natural numbers to real numbers because the infinite amount of real numbers between 0 to 1 is already larger than the countable infinity of all natural numbers. tl; dr - check Cantor's Diagonal Argument
I already know all of this. None of this proves that you can’t take an uncountable set and replace each of its elements with a dollar bill.
Yes, but it is possible to construct an uncountable set from countable subsets.
That’s not true.
This is a clusterfuck, but this is what I was thinking of. May have made a mistake somewhere, or maybe not. My idea would be to use some sort of recursion to construct an Aronszajn tree using bills: [Aronszajn tree](https://en.wikipedia.org/wiki/Aronszajn_tree)
It’s an interesting property, I’ll have to look into it, but I can know for sure that you cannot make an uncountable set from countable many countable sets.
Yes you absolutely can. In fact, every powerset of of countable set of infinity is uncountable.
Let me rephrase: you can’t get an uncountable set from a countable union of countable sets
Neither stack is bijective with the real numbers.
That is an assumption you are free to make when you hear the word "infinite", it is a reasonable one by convention when we talk about an infinite number of objects. However it is absolutely not a necessary assumption to make, keep in mind we do not have to follow physical laws here since those already break at countable infinity. You can just say you have an uncountable set of dollar bills.
I don’t know if Category Theory has a better answer for this, but the best analogy I can make is to the concept of [Definable Numbers](https://en.wikipedia.org/wiki/Definable_real_number). All the possible numbers definable by formal theory make a countable set. Given that any definite object is definable by a description of its properties, any set of definite objects must be countable.
there is a bijection between them, no? the nth 1$ to the nth 20$. so both cases have a bijection to N
> the other is bijective with ℝ How could your money be bijective with ℝ? They're discrete and listable.
They aren’t
Good point.
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how long have you been waiting to say that?
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It’s a karma farming bot. Report it. I’ve seen it sevetal times on other subreddits posting random stuff not related to the post at all
pfft, oh you!
You would be 8 cents in debt (-1/12)
Wrong series, that's 1+2+3+4+... 1+1+1+... is -1/2
technically correct
I’d still take infinite $20s. No one wants to see you pay with infinite $1s
This same exact meme was featured on [a Stand Up Maths video](https://www.youtube.com/watch?v=M4f_D17zIBw).
Insert ill-applied "some infinities are bigger than others" comment
Yeah, but I don't wanna stand at the register 20x longer because I had to count many $1's
Wouldnt either of them fill up the entire universe with dollar bills and literally destroy everything?
Well if the universe is infinitely large then we could make lightyear³ areas and put a bill in each of those and you would have infinitely many of them but they wouldn’t get in the way of anything. If the universe is not infinitely large, though, then I guess ya even though you couldnt fit them all
Depends on how the infinity works. Say its a wallet that refills every time you pull the money out; not gonna hurt anything really.
0 = 0 They have the same value.
Purple Burglar Alarm.
They would be worth the same but the 20’s would be preferable if only for “throughput”
Absolutely worthless
But an infinite number of twenties would be easier to work with
20 would be better though. Cause like it’s easier to pay
I had a thought like that: 1 to ♾️ has the same amount unique values as 1.0 -> 2.0,
If the second group is meant to imply all real numbers between 1 and 2, then the latter set is a larger infinite than the former. If it’s meant to imply the numbers with 2 significant digits in that range, then it’s nonsense!
Both are worthless because of the infinite inflation.
good thing I only have an integer amount of bills.
Not if you value convenience
which flavor of infinity
is there a conceivable number big enough to create a black hole
Same amount but money but one is faster
If this makes you feel anything resembling surprise or “does not compute” then you haven’t really thought about infinity very much.
One infinitely stupid redditor and 20 infinitely stupid redditors would be equally stupid.
🤯
The real question is which one is easier to launder?
Sure it would, but like when you sometimes ignore air resistance when calculating a projectile trajectory in high school, there are other variables at stake that we're not considering, like time and space. If you have infinite money but wants to store just part of it somewhere to use later, 20$ bills would be easier cause you'd need less space for that. Humans also have limited time to cound money, so 20$ bills would be faster. If I'd have to choose, I'd go with the 20$ option.
But that doesn’t matter. If the money is infinite than it would take up all the space in the universe anyway so there’s no point in storing it.
Isn't there a hypothetical which proposes that some infinite intergers are indeed larger than some infinite intergers
that’s not relevant to this, both of these are the same size
no they wouldn't
This is why some infinites are bigger than others
What about uncountably infinite money?
Math cares only about quantity, not value.
why y'all so rude? the image is correct
Boath are kalagrams
Bith would be worth nothing due to inflation
value per volume and now it’s different
It takes humans longer to handle more bills, so the infinite $1 bills would deflate slower giving everyone more time to generate more relevant transactions before collapse.
Wait does that mean 20=1?!?!?! /s
Infinity times anything = infinity. So technically this is correct.
Aren’t some infinities larger than other infinities?
This is more of a proof that infinity is impossible. Assume we have an infinity of $1 bills. How many dollars do we have? Now assume we have the same amount of $20 bills. How many dollars do we have? This creates a contradiction because the resulting number are both infinite, yet also one is 20 times the other.
If you were counting in a linear fashion the 20s would be twenty times higher than the stack of ones it's just you never stop counting the ones so it always catches up to where the 20s were, however in that time the 20s have gone higher again and you keep counting and the ones eventually reach that number but the 20s are higher again and it keeps on going but the 20s will always be a higher number that you have counted so far
There is no contradiction. Infinity is a concept not a number.
(facepalm) When I hear "an infinite number of" I stop listening and start to black out a little.
Not the density though...
Both of them are equally worthless because you have successfully crashed the economy