Sombyr, 1 year ago

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.