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.
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!
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
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”.
Yeah, we can still however analyze the statement f(x)=100x$/1x$ lim(x->inf) and clearly come to the conclusion that as the number of bills x approaches infinity will be equal to 100.
However, limes exists as a tool to avoid infinities and this exact problem when using calculus for practical applications - and as such it doesn’t apply here.
Screw that! I’m the man who’s gonna burn your house down! With the lemons! I’m gonna get my engineers to invent a combustible lemon that burns your house down!
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!
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.
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.
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 = ∞.
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
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. en.m.wikipedia.org/wiki/Hyperreal_number
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)
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.
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
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.
Except you’re given an infinite amount of bills, not money in the bank. So even when moving the money to the bank you’d be able to access it quicker with the 100s
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.
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.
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.
If you manage to keep an infinitely large stack of bills a secret, sure. Once somebody notices and word gets out, I’m doubtful it doesn’t get devalued in a hurry. Since these are bills that we are assuming are valid, it’s going to seem like the central bank is printing money with abandon. Famously not great for public confidence in a currency. Why would I keep my wealth in a currency that somebody has an infinite amount of? They may not be spending it today, but who knows when that changes? I’d certainly be scrambling to convert mine to something else.
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 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.
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.
Add comment