Making Money Disappear Through Infinite Iteration

This puzzle is too fun! Comments about infinite greed and Zimbabwean currency make themselves, but the conclusion is too stunning to be believed.

XOR's Hammer

In Joel David Hamkin’s paper Supertasks and Computation, he relates the following puzzle: Suppose that you have a countable infinity of dollar bills, and one day you meet the devil, who offers you the following bargain: In the first half minute from now, the devil will give you two dollar bills, and take one from you in return. In the quarter minute after that, the devil again gives you two dollar bills, and takes one from you in return. And so on, in the eighth of a minute after that, and the sixteenth of a minute after that, etc. After a minute, the whole transaction is complete. Should you take this bargain?

The answer is “no” and the reason is that the devil could do the following: Think of the bills you have at the start as being numbered 1, 3, 5, etc. and imagine that the devil has…

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