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6/12/2025, 3:50:37 AM
>>16695593
If you allow multisets or labeled numbers, then you can biject P^{1/2, 1/2, 1/2...} with {1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8...} to show that Oresme's proof (the precursor to Cauchy condensation on divergent series) doesn't work in the limit because |N| < |P^N|. For some reason it occasionally makes people seethe when you point this out.
If you allow multisets or labeled numbers, then you can biject P^{1/2, 1/2, 1/2...} with {1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8...} to show that Oresme's proof (the precursor to Cauchy condensation on divergent series) doesn't work in the limit because |N| < |P^N|. For some reason it occasionally makes people seethe when you point this out.
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