If I had a nickel for every nickel I have, I'd soon be drowned in nickels, and then be swallowed by a black hole from the infinite mass of nickels accumulated.
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For example, all possible odd numbers is an infinite that is smaller than all whole numbers. When you add in irrational numbers, it's even bigger! Here's a fun YouTube video.
It’s a divergent series, so as time approaches infinity, so does the mass. At any finite moment in time, the mass of nickels also remains finite (just really really really big!)
Of course this does not take into account gravity and the affects of special relativity, so perhaps that’s where mass approaches infinity via singularity weirdness.
Yet the mass does not need to be infinite for the density to be infinite! It just needs to be dense enough to collapse into an infinitesimally small point.
You're supposed to make the wager to a Chinese emperor where one day you have two nickles, then the next you're given four more, then the next, eight. Exponentially more nickles is easier to manage and you can bankrupt a kingdom in a few years.
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For example, all possible odd numbers is an infinite that is smaller than all whole numbers. When you add in irrational numbers, it's even bigger! Here's a fun YouTube video.
https://m.youtube.com/watch?v=SrU9YDoXE88&pp=ygUPVnNhdWNlIGluZmluaXRl
(Math degree)