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

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.

Infinity is not a number. Infinity is infinity.

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

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

nah aah, infinity plus 1 is more, I win

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.

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

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

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

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.

∞ = ∞ x 2

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

Which weighs more?

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

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.

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

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