Wikipedia:Reference desk/Archives/Mathematics/2023 August 31

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August 31

Russell sets and Russell numbers

See Russell's paradox, can sets that are not members of themselves be called “Russell sets”? Besides, can positive integers in (sequence A053169 in the OEIS) be called “Russell numbers”? 118.170.32.242 (talk) 11:23, 31 August 2023 (UTC)

Russell set is a redirect to Russell's paradox, but the term is not defined (and doesn't even occur) there; the definition should be added (by someone who knows about these things) or the redirect deleted. The German article does define it as the set of sets that are not members of themselves, i.e. the set $R$ (it points out that these are actually classes, not sets). So there is only one Russell set. As to the second question: probably not because this sequence lives entirely within OEIS, which Russell didn't even know about. --Wrongfilter (talk) 16:03, 31 August 2023 (UTC)

Going backwards from percentages to fractions

I'm not a mathematician, but this is a real-world problem that's been thrown at me:

Someone has sent me a list of (really strangely expressed) percentages and it seems to me a fair guess that they started by dividing into fractions, then calculated what those fractions were expressed as percentages. I feel sure it would be easier for everyone to understand if I express the answer as fractions rather than percentages. Now, I can easily calculate a percentage from a fraction: but I'm not aware of any method of going the other way. Does anyone have any thoughts? Here is the list:

• nine and one sixth percent
• nine and one sixth percent
• five percent
• five percent
• thirteen and one third percent
• thirteen and one third percent
• thirteen and one third percent
• ten and five ninths percent
• ten and five ninths percent
• ten and five ninths percent

Any thoughts? (By my calculation they do add up to exactly 100, which is a start). AndyJones (talk) 14:40, 31 August 2023 (UTC)

• I have another clue, if it helps. It seems they wanted the aggregate of the first second fifth sixth and seventh items on the list to be seven twelfths of the total and the aggregate of items three four eight nine and ten to be five twelfths. Which by my calculation, they are. AndyJones (talk) 14:56, 31 August 2023 (UTC)

@AndyJones: nine and one sixth percent = (9+1/6)/100 = (9*6/6+1/6)/100 = (9*6+1)/6/100 = 55/600 = 11/120. You can also enter (9+1/6)/100 in a suitable math program which will compute 11/120 for you, for example PARI/GP which has an online evaluator at https://pari.math.u-bordeaux.fr/gp.html. The least common multiple of the denominators is 360 which is the number of degrees in a circle so maybe it started with angles with integer degrees adding up to a circle, like a pie chart. PrimeHunter (talk) 15:11, 31 August 2023 (UTC)

Wow, that's brilliant. Solved it! 33/360ths, 18/360ths, 48/360ths and 38/360ths are all I need. Great work, thank you @PrimeHunter:. AndyJones (talk) 15:43, 31 August 2023 (UTC)