# Devils and Infinity [duplicate]

You are in hell for all eternity and the devil gives you two dollar bills every day with increasing serial numbers. He then takes the dollar bill you have with the smallest serial number. At the end of your infinite stay in hell, do you have infinite money or no money?

The intuitive answer for me was that if you look at the partial sums, on the Nth day you'll have $$N$$ dollars. So clearly after infinity days you should have infinity dollars.

On the other hand, you can also prove that for every dollar you ever received, there's a corresponding day that the devil takes it back, leaving you with nothing in the end.

Which one is the right answer?

## marked as duplicate by Asaf Karagila♦Oct 1 '18 at 13:13

Let's say the serial numbers are just counting. I.e.: $1,2,3...$. in this form we can see that he takes at day $m$ the dollar with the serial number $m$
Now let's say at the end you left with a dollar bill, this dollar bill will have a serial number, $n$, that means you day $n$ didn't passed, that is impossible because you are there to eternity. So you will have no money at the end