Say you win a lottery, and the organizers offer to pay the taxes on your winnings. The extra payments for the tax are taxable too right? How many iterations of paying taxes on taxes do the organizers have to go through before they truly "pay your taxes"?
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Zeno’s lottery.
It’s cute but the answer is that if the tax rate is 15% they just pay you 1/(1-15%) and call it done.
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The cute answer is that they pay you 15% on your winnings, then 15% of that amount etc until it comes out to less than a cent, which happens in N = log(0.01/W)/log(T) iterations where W is the winnings and T is the tax rate.
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So e.g. 10 iterations if you win a million bucks with a 15% tax rate.
End of conversation
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