Wikipedia:Reference desk/Archives/Mathematics/2023 June 28

= June 28 =

Dead irrational numbers
Does Wikipedia have lots of articles that mention dead irrational numbers?? What I mean is, irrational numbers once conjectured to exist but that have been defeated by proof that they're rational. There's information on one such number already; it starts 1.08366 (and after that it is meaningless because it was just a conjecture; the actual number is the exact integer 1.) Note the reason I'm calling it dead; it is because we can't explore more of the number's properties. In this case, we can't extend the 1.08366... constant to 50 decimal places the way we can with pi or the square root of 2. Georgia guy (talk) 16:18, 28 June 2023 (UTC)


 * So, you are referring to Legendre's constant, right? GeoffreyT2000 (talk) 16:26, 28 June 2023 (UTC)
 * Yes; I'm using it as an example. Georgia guy (talk) 16:34, 28 June 2023 (UTC)
 * Unfortunately I don't think this happens too often, or at least not without delving into many widespread and often far-flung niches of math. This stack exchange post does talk exactly about what you're looking for, but it seems to be more often the case that a value thought to be rational is actually irrational. GalacticShoe (talk) 18:04, 28 June 2023 (UTC)


 * Note that Legendre did not conjecture that the constant $$B$$ of which he is the eponym is irrational. He merely observed that putting $$B=1.08366$$ resulted in an approximation with a "very satisfying accuracy". --Lambiam 20:11, 28 June 2023 (UTC)
 * If Euler's constant $$\gamma$$ turn out to be rational, then it will be such number? 118.170.48.206 (talk) 13:44, 4 July 2023 (UTC)
 * I think so, yes. It would be the surprise of the millenium. The nominator and denominator will then be greater than 1050000. --Lambiam 14:18, 4 July 2023 (UTC)