An infinite number of $1 bills and an infinite number of $20 bills would be worth the same
Not true! Infinities can be different sizes! Take, for example, the set of whole numbers: [1,2,3,4….]. It’s infinite! But look at the set of even numbers [2,4,6…]. It’s also infinite.
But, the set of whole numbers is bigger than the set of even numbers. They’re both infinite, but one is a bigger infinity.
Math is great.
It gets weirder. They WOULD be worth the same, because they would all have ZERO MONETARY VALUE.
A medium of exchange must be finite in order that it can be mapped onto finite goods and services. If you had an infinite number of dollar bills, hyperinflation would render any finite number of them worthless. They wouldn’t even be worth the paper they’re printed on, since with an infinite supply of a resource, the marginal value of any finite subsection of it is zero.
Wouldn’t they be worth exactly the paper they’re printed on, since the paper’s value would now also be zero for the same reason?
@esser-z im pretty sure thats literally incorrect. infinites is the same
@queernightmare can u verify
@37q that’s like a pretty disputed paradox within mathematics but i think the general consensus is in favor of there being infinities of different sizes. i think it’s a moot point personally but i’m not a mathematically inclined at all
The main argument I’ve heard of in terms of differently sized infinities is between countable versus uncountable infinities and like… all of the infinite series / situations listed here are countable infinities so I’m not sure that that applies?
