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.

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.

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

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

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.

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.

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.

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

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

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.

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

Which weighs more?

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

nah aah, infinity plus 1 is more, I win

∞ = ∞ x 2

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.

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

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

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?

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.

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

This meme was made by thr guy on the left thinking he was thr guy on the right.

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

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

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

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.

Infinity is not a number.

Tbh I think this is correct. Not necessarily mathematically, idk maths, but realistically paying with infinite 100$ Bills is easier than with 1$ Bills. Therefore it saves time and so the .infinite 100$ Bills are worth more

Might just be me.

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

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've solved inflation!

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 must be that "autism" I've been hearing so much about

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.