memes

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.

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.

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.

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".