StatOps

Infinity is a funny concept. I can give you infinitely many things while at the same time taking away infinitely many things and leave you with nothing, infinitely many things, or any number of things I want!

Think about this scenario: It's one second to noon. I give you ten gold coins (number them 1-10) and take away the first gold coin I gave you (number 1). At 1/2 second to noon I give you another ten coins (11-20) and take away the second coin I gave you (2). If I continue giving you coins 10n-9 through 10n and taking away coin n at 1/n seconds to noon, when noon arrives you will have no coins at all! (Why? Is infinity a number, so that two times infinity is greater than infinity? Google "cardinality" to learn more.)

Consider this alternative scenario: Again, it's one second to noon. I give you the same gold coins (1-10), but this time I take back coins 2-10. At 1/2 second to noon I give you coins 11-20 and take back coins 12-20. If I continue doing this, at noon you will have infinitely many gold coins!

So in one case I gave you ten and took back one each time and left you with nothing, and in the other case I gave you ten and took back nine and left you with infinite coins! (What mathematical concept suggests I can leave you with any number of coins I like? What happens if the coins are indistinguishable?)