Hilbert Hotel - The Grand Reopening
summary
A hotel changes room rates so nightly incomes follow a rearranged harmonic sequence, producing infinite income but zero tax after applying a specific wiring algorithm: send the next positive payment, then enough negatives to bring the running total ≤ 0, repeat. Proof uses comparison to integrals to show divergence of positives and negatives separately and invokes the Riemann rearrangement theorem to explain how a conditionally convergent series can be forced to any sum. Tax inspector appears; the scheme works mathematically.
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