Infinity aside, the growth rate of number of bills vs the value of those bills has nothing to do with the original scenario though. It’s like arguing that a kilogram of feathers weighs less than a kilogram of bowling balls because the scale goes up less for every feather I put on the scale compared to every bowling ball I put on the scale.
Edit: Though if you want to talk about how weird infinity really is, here are some fun facts for you:
There are just as many even numbers as rational numbers, even though all even numbers are rational but not all rational numbers are even. This is because both sets are countably infinite.
There are more irrational numbers than rational numbers. This is because even though both sets are infinite, the set of irrational numbers is uncountably infinite.
It’s like arguing that a kilogram of feathers weighs less than a kilogram of bowling balls because the scale goes up less for every feather I put on the scale compared to every bowling ball I put on the scale.
I’m arguing that infinity bowling balls weighs more than infinity feathers, though
Try thinking of it like this: If I have an infinite amount of feathers, I can balance a scale that has any number of bowling balls on it. Even if there was an infinite number of bowling balls on the other side, I could still balance it because I also have infinite feathers that I can keep adding until it balances. I don’t need MORE than infinite feathers just because there’s infinite bowling balls. In the same way if my scale had every rational number on one side I could add enough even numbers to the other side to make it balance, but if I had all the irrational numbers on one side of the scale then I would never have enough rational numbers to make it balance out even though they are also infinite.
Edit: I suppose the easiest explaination is that it’s already paradoxical to even talk about having an infinite number of objects in reality just like it would be paradoxical to talk about having a negative number of objects. Which weighs more, -5 feathers that weigh 1 gram each or -5 bowling balls that weigh 7000 grams each? Math tells us in this case that the feathers now weigh more than the bowling balls even though we have the same amount of each and each bowling ball weighs more than each feather. In reality we can’t have less than zero of either.
Infinity aside, the growth rate of number of bills vs the value of those bills has nothing to do with the original scenario though. It’s like arguing that a kilogram of feathers weighs less than a kilogram of bowling balls because the scale goes up less for every feather I put on the scale compared to every bowling ball I put on the scale.
Edit: Though if you want to talk about how weird infinity really is, here are some fun facts for you:
There are just as many even numbers as rational numbers, even though all even numbers are rational but not all rational numbers are even. This is because both sets are countably infinite.
There are more irrational numbers than rational numbers. This is because even though both sets are infinite, the set of irrational numbers is uncountably infinite.
I’m arguing that infinity bowling balls weighs more than infinity feathers, though
Try thinking of it like this: If I have an infinite amount of feathers, I can balance a scale that has any number of bowling balls on it. Even if there was an infinite number of bowling balls on the other side, I could still balance it because I also have infinite feathers that I can keep adding until it balances. I don’t need MORE than infinite feathers just because there’s infinite bowling balls. In the same way if my scale had every rational number on one side I could add enough even numbers to the other side to make it balance, but if I had all the irrational numbers on one side of the scale then I would never have enough rational numbers to make it balance out even though they are also infinite.
Edit: I suppose the easiest explaination is that it’s already paradoxical to even talk about having an infinite number of objects in reality just like it would be paradoxical to talk about having a negative number of objects. Which weighs more, -5 feathers that weigh 1 gram each or -5 bowling balls that weigh 7000 grams each? Math tells us in this case that the feathers now weigh more than the bowling balls even though we have the same amount of each and each bowling ball weighs more than each feather. In reality we can’t have less than zero of either.