EDIT: I THINK I STAND CORRECTED

I got tired of reading people saying that the infinite stack of hundreds is more money, so get this :

Both infinites are countable infinites, thus you can make a bijection between the 2 sets (this is literally the definition of same size sets). Now use the 1 dollar bills to make stacks of 100, you will have enough 1 bills to match the 100 bills with your 100 stacks of 1.

Both infinites are worth the same amount of money... Now paying anything with it, the 100 bills are probably more managable.

You could also just divide your infinite stack of $1 bills into 100 infinite stacks of $1 bills. And, obviously, an infinite stack of $100 bills is equivalent to 100 infinite stacks of $1 bills.
(I know this is only slightly different than what you're getting at, which is that infinitely many stacks of 100 $1 bills is equivalent to an infinite stack of $100 bills)
Now paying anything with it, the 100 bills are probably more managable.
I'd take the 1's just because almost everywhere I spend money has signs saying they don't take bills higher than $20.
- Yup. Exactly this.
They can spend the same amount of money, but at any moment the one with 100s has more money. If you have 2 people each picking up 1 bill at the same rate at any singular moment the person picking up the 100s will have more money.
Since we're talking about a material object like dollar bills and not a concept like money we have to take into consideration it's utility and have to keep in mind the actual depositing and spending would be at any individual moment. The person with 100s would have a much easier/quicker time using the money therefore the 100s have more utility.
- We're definitely not talking about this like a material object at the same time, though. There's no way for a single person to store and access an infinite pile of bills.
  You can spend a 100 dollar bill faster than a 1 dollar bill, sure, but both stacks would have the same money in the bank.
Alternatively for small brains like me:
Imagine you have an infinite amount of $1 bills are laid out in a line. Right next to it is a line of $100 bills.
As you go down the line, count how much money you have at any given point.
Which total is worth more?
- Your example introduces the axis of time which is not in consideration when discussing infinity. You're literally removing infinity from the equation by doing that because "at any given point" by definition is not infinity. Let's say that point is 1 million bills down the line. Now you're comparing 1,000,000 x 100 vs 1,000,000 x 1, nothing to do with infinity
- Imagine the line of 1s is stacked like pages in books on a shelf, but the line of 100s is placed in a row so they're only touching on the sides. You could probably fit a few hundred 1s in the space of one 100. Both lines still have infinite bills in them, but now as you go along, you're seeing a lot more 1s at a time.
  That's the thing about infinities, you can squish and stretch them, and they're still infinite.

This kind of thread is why I duck out of casual maths discussions as a maths PhD.

The two sets have the same value, that is the value of both sets is unbounded. The set of 100s approaches that value 100 times quicker than the set of singles. Completely intuitive to someone who’s taken first year undergraduate logic and calculus courses. Completely unintuitive to the lay person, and 100 lay people can come up with 100 different wrong conclusions based on incorrect rationalisations of the statement.

I’ve made an effort to just not participate since back when people were arguing Rick and Morty infinite universe bollocks. “Infinite universes means there are an infinite number of identical universes” really boils my blood.

It’s why I just say “algebra” when asked what I do. Even explaining my research (representation theory) to a tangentially related person, like a mathematical physicist, just ends in tedious non-discussion based on an incorrect framing of my work through their lens of understanding.

For what it's worth, people actually taking the time to explain helped me see the error in my reasoning.
- There’s no problem at all with not understanding something, and I’d go so far as to say it’s virtuous to seek understanding. I’m talking about a certain phenomenon that is overrepresented in STEM discussions, of untrained people (who’ve probably took some internet IQ test) thinking they can hash out the subject as a function of raw brainpower. The ceiling for “natural talent” alone is actually incredibly low in any technical subject.
  There’s nothing wrong with meming on a subject you’re not familiar with, in fact it’s often really funny. It’s the armchair experts in the thread trying to “umm actually…” the memer when their “experience” is a YouTube video at best.
- I don't know why you see it as an error. It's the format of the meme. The guy in the middle is right, the guy on the left is wrong. That's just how this meme works. But the punchline in this meme format is the the guy on the right agrees with the wrong guy in an unexpected way. I'm with the guy on the right and no appeals to Schröder–Bernstein theorem is going to change my mind.
Yeah I sell cabinets and sometimes people are like “How much would a 24 inch cabinet cost?”
It could cost anything!
Then there are customers like “It’s the same if I just order them online right?” and I say “I wouldn’t recommend it. There’s a lot of little details to figure out and our systems can be error probe anyway…” then a month later I’m dealing with an angry customer who ordered their stuff online and is now mad at me for stuff going wrong.
The two sets have the same value, that is the value of both sets is unbounded. The set of 100s approaches that value 100 times quicker than the set of singles.
Hey. Sorry, I'm not at all a mathematician, so this is fascinating to me. Doesn't this mean that, once the two sets have reached their value, the set of 100 dolar bills will weigh 100 times less (since both bills weigh the same, and there are 100 times fewer of one set than the other)?
If so, how does it reconcile with the fact that there should be the same number bills in the sets, therefore the same weight?
- I like this comment. It reads like a mathematician making a fun troll based on comparing rates of convergence (well, divergence considering the sets are unbounded). If you’re not a mathematician, it’s actually a really insightful comment.
  So the value of the two sets isn’t some inherent characteristic of the two sets. It is a function which we apply to the sets. Both sets are a collection of bills. To the set of singles we assign one value function: “let the value of this set be $1 times the number of bills in this set.” To the set of hundreds we assign a second value function: “let the value of this set be $100 times the number of bills in this set.”
  Now, if we compare the value restricted to two finite subsets (set within a set) of the same size, the subset of hundreds is valued at 100 times the subset of singles.
  Comparing the infinite set of bills with the infinite set of 100s, there is no such difference in values. Since the two sets have unbounded size (i.e. if we pick any number N no matter how large, the size of these sets is larger) then naturally, any positive value function applied to these sets yields an unbounded number, no mater how large the value function is on the hundreds “I decide by fiat that a hundred dollar bill is worth $1million” and how small the value function is on the singles “I decide by fiat that a single is worth one millionth of a cent.”
  In overly simplified (and only slightly wrong) terms, it’s because the sizes of the sets are so incalculably large compared to any positive value function, that these numbers just get absorbed by the larger number without perceivably changing anything.
  The weight question is actually really good. You’ve essentially stumbled upon a comparison tool which is comparing the rates of convergence. As I said previously, comparing the value of two finite subsets of bills of the same size, we see that the value of the subset of hundreds is 100 times that of the subset of singles. This is a repeatable phenomenon no matter what size of finite set we choose. By making a long list of set sizes and values “one single is worth $1, 2 singles are worth $2,…” we can define a series which we can actually use for comparison reasons. Note that the next term in the series of hundreds always increases at a rate of 100 times that of the series of singles. Using analysis techniques, we conclude that the set of hundreds is approaching its (unbounded) limit at 100 times the rate of the singles.
  The reason we cannot make such comparisons for the unbounded sets is that they’re unbounded. What is the weight of an unbounded number of hundreds? What is the weight of an unbounded number of collections of 100x singles?
- once the two sets have reached their value
  will weigh 100 times less
  there should be the same number bills in the sets
  The short answer is that none of these statements apply the way you think to infinite sets.
- I see what you did here...
So to paraphrase, the raging person in the middle is right? I'll take your answer no questions asked.
- In short, yes.
Correct me if I'm wrong, but isn't it that a simple statement(this is more worth than the other) can't be done, since it isn't stated how big the infinities are(as example if the 1$ infinity is 100 times bigger they are worth the same).
- Sorry if you've seen this already, as your comment has just come through. The two sets are the same size, this is clear. This is because they're both countably infinite. There isn't such a thing as different sizes of countably infinite sets. Logic that works for finite sets ("For any finite a and b, there are twice as many integers between a and b as there are even integers between a and b, thus the set of integers is twice the set of even integers") simply does not work for infinite sets ("The set of all integers has the same size as the set of all even integers").
  So no, it isn't due to lack of knowledge, as we know logically that the two sets have the exact same size.
If we only consider the monetary value, both "briefs" have the same value. Otherwise if we incorporate utility theory with a concave bounded utility curve over the monetary value and factor in other terms such as ease of payments, or weight (of the drawn money) then the "worth" of the 100 dollar bills brief could be greater for some people. For me, the 1 dollar bills brief has more value since I'm considering a potential tax evasion prosecution. It would be very suspicious if I go around paying everything with 100 dollar bills, whereas there's a limit on my daily spending with the other brief (how many dollars I can count out of the brief and then handle to the other person).
- I admit the only time I've encountered the word utility as an algebraist is when I had to TA Linear Optimisation & Game Theory; it was in the sections of notes for the M level course that wasn't examinable for the Bachelors students so I didn't bother reading it. My knowledge caps out at equilibria of mixed strategies. It's interesting to see that there's some rigorous way of codifying user preference. I'll have to read about it at some point.

They're both countibly infinite thus the same, no?

Theoretically, yes. Functionally, no. When you go to pay for something with your infinite bills, would you rather pay with N number of 100 dollar bills or get your wheelbarrow to pay with 100N one dollar bills? The pile may be infinite, but your ability to access it is finite. Ergo, the "denser" pile is worth more.
- If we’re adding real world hypotheticals you would be paying for your shit on card anyway. You just go to the bank with how ever many truck loads of $100 bills when ever you needed a top up. Secondly you wouldn’t be doing it yourself, you pay someone else to do it. Thirdly as soon as the government found out you effectively had a money printer they would put you in prison or disappear you to prevent you from collapsing their money system, not to mention the serial numbers on the notes would have to be fraudulent because they wouldn’t match up with mints. And finally any physical object with an infinite quantity would be the size of the universe, likely causing either black hole or destroying the universe and us along with it. So in closing what sounds like a great situation is probably worth any potential risk
- Yeah, this is what it comes down to. In calculus, infinity doesn't exist, you just approach it when you take the limit. You'll approach it "quicker" with the 100 dollar bills, so to speak
To establish whether one set is of a larger cardinality, we try to establish a one-to-one correspondence between the members of the set.
For example, I have a very large dinner party and I don't want to count up all the forks and spoons that I'll need for the guests. So, instead of counting, everytime I place a fork on the table I also place a spoon. If I can match the two, they must be an equal number (whatever that number is).
So let's start with one $1 bill. We'll match it with one $100 bill. Let's add a second $1 bill and match it with another $100 bill. Ad infinitum. For each $1 bill there is a corresponding $100 bill. So there is the same number of bills (the two infinite sets have the same cardinality).
You likely can see the point I'm making now; there are just as many $1 bills as there are $100 bills, but each $100 bill is worth more.
- You could make an argument that infinite $100 bills are more valuable for their ease of use or convenience, but infinite $100 bills and infinite $1 bills are equivalent amounts of money. Don't think of infinity as a number, it isn't one, it's infinity. You can map 1000 one dollar bills to every single 100 dollar bill and never run out, even in the limit, and therefore conclude (equally incorrectly) that the infinite $1 bills are worth more, because infinity isn't a number. Uncountable infinities are bigger than countable ones, but every countable infinity is the same.
  Another thing that seems unintuitive but might make the concept in general make more sense is that you cannot add or do any other arithmetic on infinity. Infinity + infinity =/= 2(infinity). It's just infinity. 10 stacks of infinite bills are equivalent to one stack of infinite bills. You could add them all together; you don't have any more than the original stack. You could divide each stack by any number, and you still have infinity in each divided stack. Infinity is not a number, you cannot do arithmetic on it.
  100 stacks of infinite $1 bills are not more than one stack of infinite $1 bills, so neither is infinite $100 bills.
- I don't see what you are trying to say. You can also match 200 $1 bills with each $100 bill. The correspondence does not need to be one-to-one.
- but each $100 bill is worth more.
  But the meme doesn't talk about the value of each $100 bill; it talks about the value of the bills collectively.
- I think you're misunderstanding the math a bit here. Let me give an example.
  If you took a list of all the natural numbers, and a list off all multiples of 100, then you'll find they have a 1 to 1 correspondence.
  Now you might think "Ok, that means if we add up all the multiples of 100, we'll have a bigger infinity than if we add up all the natural numbers. See, because when we add 1 for natural numbers, we add 100 in the list of multiples of 100. The same goes for 2 and 200, 3 and 300, and so on."
  But then you'll notice a problem. The list of natural numbers already contains every multiple of 100 within it. Therefore, the list of natural numbers should be bigger because you're adding more numbers. So now paradoxically, both sets seem like they should be bigger than the other.
  The only resolution to this paradox is that both sets are exactly equal. I'm not smart enough to give a full mathematical proof of that, but hopefully that at least clears it up a bit.
  Adding up 100 dollar bills infinitely and adding up 1 dollar bills infinitely is functionally exactly the same as adding up the natural numbers and all the multiples of 100.
  The only way to have a larger infinity that I know of us to be uncountably infinite, because it is impossible to have a 1 to 1 correspondence of a countably infinite set, and an uncountably infinite set.
- You're right that they're the same size but you're mistaken when you try to assign a total value to the stack. Consider breaking each $100 bill into 100 $1 bills. The value is the same, clearly. So for each pair, you have a $1 bill and a small stack of 100 $1 bills. Now combine all singles back together in an infinite stack. Then combine all stacks of 100 into an infinite stack.
  And you know what? Both infinite stacks are identical. They have the same value.
- each $100 bill is worth more.
  But the creation of each additional bill devalues the currency. At some point the value of all this paper money is negative because it’s not worth keeping and storing. The point at which they cross from positive to negative value would give them zero value, and they’d be equal.
- You likely can see the point I’m making now; there are just as many $1 bills as there are $100 bills, but each $100 bill is worth more.
  But the monetary value of the bills in each stack still adds up to infinity for both. It's like having an uncapped Internet connection at 56 KBit/s versus 100 MBit/s: You can download all the things with both, but that alone doesn't make them equal.

Neither is bigger. Even "∞ x ∞" is not bigger than "∞". Classical mathematics sort of break down in the realm of infinity.

It was probably mentioned in other comments, but some infinities are "larger" than others. But yes, the product of the two with the same cardinal number will have the same
- Yes, uncountably infinite sets are larger than countably infinite sets.
  But these are both a countably infinite number of bills. They're the same infinity.
- I think quite some people heard of the concept of different kinds of infinity, but don't know much about how these are defined. That's why this meme should be inverted, as thinking the infinities described here are the same size is the intuitive answer when you either know nothing or quite something about the definition whereas knowing just a little bit can easily lead you to the wrong answer.
  As the described in the wikipedia article in the top level comment, the thing that matters is whether you can construct a mapping (or more precisely, a bijection) from one set to the other. If so, the sets/infinities are of the same "size".
- What about lemons?
You're the guy in the middle by the way.
This problem doesn't involve cardinal numbers.
So it’s basically just a form of NaN?

The reason infinity $100 bills is more valuable than infinity $1 bills: it takes less effort to utilize the money.

Let's say you want to buy a $275,000 Lamborghini. With $1 bills, you have to transport 275,000 notes to pay for it. That will take time and energy. With $100 bills, you have to transport 2750 notes. That's 100x fewer, resulting in a more valuable use of time and energy.

Even if you had a magical wallet that weighed the same as a standard wallet and always a had bills of that type available to pull out when you reach in. It's less energy to reach in a fewer number of times.

Let's toss in the perspective of the person receiving the money, too. Wouldn't you rather deal with 2750 notes over 275,000, if it meant the same monetary value? If you keep paying in ones, people will get annoyed. Being seen favorably has value.

Value is about more than money.

You couldn't buy that car with either denomination since money would have zero value now... and also the universe would collapse in on itself... but mainly the zero value thing.
- Money only has zero value if people wideluly know you have infinity money.
  And even then, unless you've spent huge amounts you won't meaningfully inflate the money supply.
- I think it would be easier to go to thebank now and then to exchange some of your $100 for lower value bills than to do the opposite.
  Besides, if there are places that don't take bills less than $20, there are a lot of places that aren't going to let you pay with only $1 bills. I can't imagine a car dealership letting you do that. Or if you want to buy a home, etc.
very nice! But very OT tho

I considered deleting the post

Please don't! I've been out and about today and inadvertently left this post open. I've thoroughly enjoyed reading all of the comments and it has been one of the most engaging posts I've seen on Lemmy

I appreciate all of the discussion it generated! Thank you <3

Infinity is not a number. Infinity is infinity.

People are confusing Infinity with lim x->Infinity. There's a huge difference.

The hyperreals are a formal treatment of infinite numbers. It still doesn't let people use infinity as a number in the way that posts like this suggest, but they're interesting nonetheless. https://en.m.wikipedia.org/wiki/Hyperreal_number
There’s a huge difference.
Infinitely huge?

Duh, of course it is because it's friggin hard to pay everything with 1 dollar bills, it will slowly eat away at your sanity.

Okay, I will pay you $100 for every 200 dollars you pick up out of this infinite pile and turn into $100 bills.
Now it won't drive me insane at all, and you can get as rich as you want to be.

nah aah, infinity plus 1 is more, I win

Infinity plus infinity .... Na na NA NA na!!! I win! Na na NA NA na!!!
- Infinity plus infinity, plus +1 to whatever anyone else says, recurring. No returns!!
  I think you'll find that's sealed tight now and that I win. Na NAAAA!
  /runs off maniacally
- nonono, Infinity times infinity plus one, I win! *tehee nanana Na na na! *

Seriously though, infinity is Infinity, it's not a number, it's infinity.

Yes, the amount of both stacks is infinity. The question was not "What stack is easier to pay for something with".
- Both are equally easy to pay with since ∞ - X = ∞ if we disregard that 100s are more convenient way to pay for cars.
Infinities can be different sizes (although in OPs case they are not): https://www.cantorsparadise.com/why-some-infinities-are-larger-than-others-fc26863b872f?gi=d5e83e23c757

No matter which denomination you choose, the infinite motel will always have room for another bill.

What does "worth" even mean in this set up?

I was just over here thinking this was about the practical utility of a $100 bill versus a wad of 100 $1 bills making an infinite quantity of the former preferable in comparison to (i.e. "worth more than") the latter...
- Imagine being the guy with an infinite money glitch but having to pay for EVERYTHING in one dollar bills. Buying even a modest sedan would be a pain in the ass. "What do you do for a living?" "I'm 47 strippers."

Approaching an infinite amount of steel vs. Approaching an infinite amount of feathers.

Which weighs more?

An infinite amount of AeroGel.

Value is a weird concept. Even if mathematically the two stacks should have the same value, odds are some people will consider the $100 bill stack worth more, and be willing to do more in exchange for it. That effectively does make it worth more.

The moment you bring in the concept of actually using this money to pay for things, you have to consider stuff like how easy it is to carry around, and the 100s win. If your pile is infinite then you don't even need 1s at the strip club.
An infinite stack of either would devalue the currency so as to be completely worthless. Well, perhaps worth whatever you can recycle those bills into.
- Yes and no. If you spend that infinite money, then yes. The currency would be massively devalued as you would be adding money into the economy.
  If you sat on it, nothing would happen. I imagine that the Federal Bank doesn't know about your infinite stash and therefore isn't taking into account any equation.
- The money only devalues based on how much is in circulation. You'll only devalue the currency as you spend it and you'd have to spend a trillion to have a non-minor effect.

∞ = ∞ x 2

That's not a true statement. 2∞ < ∞ and ∞ < 2∞ is how you'd write it.
Otherwise you could subtract infinity from both sides and get 0 = ∞.
- Except subtraction is not applicable in this case
- Not true. 2∞ is not bigger or smaller than ∞. This is explained by Hilbert's hotel. And subtracting infinity from infinity is undefined so you do not get 0 = ∞.

If I had infinity $100 notes I could ask to break them into 50s and have 2x infinity $50 notes. It's called winning.

False. There would still be a finite supply of $50 bills, so you could never have infinity $50 bills at any time.
- I forgot to mention they're forgeries.

An infinite number of bills would mean there's no space to move or breathe in, right? We'd all suffocate or be crushed under the pressure?

Depends on implementation.
There's a hierarchy called cardinality, and any two infinitives that can be cleanly mapped 1:1 are considered equal even if one "looks" bigger, like in the example from OP where you can map 100x 1 dollar bills to each 100 dollar bill into infinity and not encounter any "unmappable" units, etc.
So filling an infinite 3D volume with paper bills is practically equivalent to filling a line within the volume, because you can map an infinite line onto a growing spiral or cube where you keep adding more units to fill one surface. If you OTOH assumed bills with zero thickness you can have some fun with cardinalities and have different sized of infinities!
We'd all suffocate or be crushed under the pressure?
hey just like regular capitalism
I guess you'd need infinite space for an infinite number of bills. But it'd still be full to the brim?

Why are people upvoting this post? It's completely wrong. Infinity * something can't grow faster than infinity * something else.

Afaik it can, buy not this way.
I'm not mathmatician but I got explained once that there are "levels" of Infinity, and some can be larger than others, but this case is supposed to be the same level.
I dont really know much about this topic so take it with a grain of salt.
- There is an infinite amount of possible values between 0 and 1. But factorially it means measuring a coastline will lead towards infinity the more precise you get.
  And up all the values between 0 and 1 with an infinite number of decimal places and you get an infinite value.
  Or there's the famous frog jumping half the distance towards a lilly pad, then a quarter, than an eighth. The distance halfs each time so it looks like they'll never make it. An infinitesimally decreasing distance until the frog completes an infinite number of jumps.
  Then what most people understand by infinity. There are an infinite number of integers from 0 to infinity. Ultimately this infinity we tend to apply in real world application most often to mean limitless.
  These are mathematically different infinities. While all infinity, some infinities have limits.
- Something to do with the...Greek? Hebrew? Klingon? Letter Aleph
- for $1 bills: lim(x->inf) 1*x
  for $100 bills: lim(x->inf) 100*x
  Using L'Hôpital's rule, we take the derivative of each to get their ratio, ie: 100/1, so the $100 bill infinity is bigger (since the value of the money grows faster as the number of bills approaches infinity, or said another way: the ratio of two infinities is the same as the ratio of their rates of change).
Because the number of dollars is not the only factor in determining which is better. If I have the choice between a wallet that never runs out of $1 bills or one that never runs out of $100 bills, I’ll take it in units of $100 for sure. When I buy SpaceX or a Supreme Court justice or Australia or whatever, I don’t want to spend 15 years pulling bills out of my wallet.

I love how people here try to put this in practical terms like "when you need to pay something 100 is better". It's infinite. Infinite. The whole universe is covered in bills. We all would probably be dead by suffocation. It makes no sense to try to think about the practicality of it. Infinite is infinite, they are the same amount of money, that's all.

For practical use it would be better to have an infinite supply rather than an infinite amount
The whole universe is covered in bills. We all would probably be dead by suffocation.
Couldn't there just be a single line of bills stretching out to infinity?
I think it’s because there is nuance in the wording. It doesn’t say “dollar amount”, it says “worth”, and the worth of a thing can be more than its dollar amount.
Infinite hundreds is “worth more” in a sense because it’s easier to use, and that is added value!
- stahp

Similar problem: which set is bigger, the set of all real numbers, or the set of all real numbers between 0 and 1?

Not quite because it's easily shown that the set of all real numbers contains the set of all real numbers between 0-1, but the set of all real numbers from 0-1 does not contain the set of all real numbers. It's like taking a piece of an infinite pie: the slice may be infinite as well, but it's a "smaller" infinite than the whole pie.
This is more like two infinite hoses, but one has a higher pressure. Ones flowing faster than the other, but they're both flowing infinitely.
- actually you can for each real number you can exhaustively map a uninque number from the interval (0,1) onto it. (there are many such examples, you can find one way by playing around with the function tanx)
  this means these two sets are of the same size by the mathematical definition of cardinality :)
- That's not really how counting infinite sets works.
  Suppose you have the set {1,2,3} and another set {2,4,6}. We say that both sets are of equal cardinality because you can map each element in the first set to a unique element in the second set (the mapping is "one to one"/injective), and every element has something mapped to it (the mapping is onto/surjective).
  Compare the number of integers to the number of even integers. While it intuitively seems like there should be more integers than even integers, that's not actually the case. If you map 1 to 2, 2 to 4, 3 to 6, 4 to 8, ..., n to 2n, then you'll see both sets actually have the same number of things in them because that mapping is one to one and onto.
  There's similarly the same number of real numbers as numbers between 0 and 1.
  But there's more numbers between 0 and 1 than there are integers.
- Actually, the commenter is exactly right. The real line does contain the open interval (0,1). The open interval (0,1) has the exact same cardinality as the real numbers.
  An easy map that uniquely maps a real number to a number of the interval (0,1) is the function mapping x to arctan(x)/π + 1/2. The existence of a bijection proves that the sets have the same size, despite one wholly containing the other.
  The comment, like the meme, plays on the difference between common intuition and mathematical intuition.
- It's a similar problem. Both are infinity but one is a bigger infinity than the other.

I'd rather have 100 dollar bills rather than 1 dollar bills.

I wouldn't. Most places refuse to take $100s due to rampant counterfeiting, and banks don't bat an eye at a huge stack of ones as a deposit. To just flow through life, a limitless supply of ones is far easier to deal with than any amount of crisp $100 bills. Inflation might change this, but probably not in my lifetime.
- Most places where you live. This isn't a problem for the entire globe. Some of it, sure. But not all of it. I pay with hundreds all the time in Australia and noone gives a shit.

Really depends on whether the infinite store will break hundreds for you.

There is a lot of very confident, opposing answers here...

I'm super confused. It seems most of this conversation misses the meme format. Everyone is agreeing with the middle guy. That's how the meme works. The middle guy is right, but that's not the point. It's like I'm taking crazy pills.
- The point of the meme format is not that the middle guy is right. It's the opposite.

It depends what worth entails - if it's just the monetary value then yeah they're the same, but if the worth also comes from desirability and convenience, then infinite stack of 100 dollar bills would be way more desirable when compared to 1 dollar bills.

Less space needed to carry the money around (assuming it's stored in some negative space and you just grab a bunch of bills when you wanna buy something), faster to take the bills for higher value items and easier to count as well.

This is especially true if you live in a place where the 1 dollar option would mean infinite coins rather than bank notes. :P
- But then you can imagine you found a pirate's chest with all the coins inside 🤩

Infinity is not a number.

Actually, it's just an eight on its side. You need to get your facts checked.
- I've been a fool
As a mathematician, I tend to disagree with this common truism because it limits one's ability to think about transfinites and suggests there's a widely agreed upon technical definition of "number".
- There is, though. Maybe not wide in your inner circle, but very, very wide if you actually look around.

Thank you for the edit, I was really starting to be confused. And kudos to keeping it up and clarifying, I wish there were more people like you!

The people struggling with this are the same ones that think a ton of lead is heavier than a ton of feathers

You can have infinities of different sizes
- You can. This is not one of them

You've solved inflation!

Just wanna say I have mad respect for you for acknowledging that you were wrong, but leaving the post up. I wish more people were as brave as you are

Wouldn't an infinite number of anything with physical mass collapse the universe as we know it and challenge our models of physics? But yeah sign me up for the Benjamin's.

https://youtu.be/fNjhJrXG36A?si=bMU1JIWPGpq8CtxV

Really seeing the iq spread here

This is wrong. Having an infinite amount of something is like dividing by zero - you can't. What you can have is something approach an infinite amount, and when it does, you can compare the rate of approach to infinity, which is what matters.

I'd argue that infinite 1 bills are worth less than infinite 100 bills. Because infinite 100 is infinite 1 times infinite 100. Even though they effectively turn into the same amount that is infinity.