An infinite number of $1 bills and an infinite number of $20 bills would be worth the same
No? Because the base number is different so you would need 20 one dollar bills for each 20 dollar bill or you need the 20 dollar bills to be capped at a point but regardless it wouldn’t be the same
Alas no - just-shower-thoughts has the right of it here. In much the same way that there are the same number of integers and rational numbers despite integers being a subset of rational numbers.
If infinity isn’t hurting your brain, you’re doing it wrong.
I see lot of people going “no, because infinities can be different sizes!” and like, yeah, but you don’t get from one to another by multiplying every value by 20. That just makes an equally large countable set, by definition.
Yeah. You stay in the same cardinality by multiplying infinity by a number. Going to a different cardinality takes much more than that.
if you havine infinite $1 bills that means you have infinite money as in you have money that is constanty replenishing itself. The same applies if it’s $20 bills. In both cases you would have money that replenishes indefinately so you would have the same amount of money. with infinite $1 bills you can get $100 by having 100 of them. With infinite $20 bills you can get $100 with five of them. it’s still the same amount of money.