I considered deleting the post, but this seems more cowardly than just admitting I was wrong. But TIL something!
this post was submitted on 06 Jan 2024
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Theoretically, yes. Functionally, no. When you go to pay for something with your infinite bills, would you rather pay with N number of 100 dollar bills or get your wheelbarrow to pay with 100N one dollar bills? The pile may be infinite, but your ability to access it is finite. Ergo, the "denser" pile is worth more.
If we’re adding real world hypotheticals you would be paying for your shit on card anyway. You just go to the bank with how ever many truck loads of $100 bills when ever you needed a top up. Secondly you wouldn’t be doing it yourself, you pay someone else to do it. Thirdly as soon as the government found out you effectively had a money printer they would put you in prison or disappear you to prevent you from collapsing their money system, not to mention the serial numbers on the notes would have to be fraudulent because they wouldn’t match up with mints. And finally any physical object with an infinite quantity would be the size of the universe, likely causing either black hole or destroying the universe and us along with it. So in closing what sounds like a great situation is probably worth any potential risk
Yeah, this is what it comes down to. In calculus, infinity doesn't exist, you just approach it when you take the limit. You'll approach it "quicker" with the 100 dollar bills, so to speak
You're thinking of a different calculus problem in this case we are comparing the growth rate of
100*\infty vs \infty. In calculus, you cannot accelerate the growth of \infty. If you put\infty / \inftyyour answer will beundefined(you can double check with Wolfram), similarly, if you put100*\infty / \infty, you will also getundefined