Comment by senfiaj

8 hours ago

> Euler's constant, gamma = 0.577215 ... = lim n -> infinity > (1 + 1/2 + 1/3 + 1/4 + ... + 1/n - ln(n)) (Not proven to be transcendental, but generally believed to be by mathematicians.)

So why bring some numbers here as transcendental if not proven?

10 comments

senfiaj

Reply
auggierose  8 hours ago

Because it still might be transcendental. Just because you don't know if the list is correct, doesn't mean it isn't.

  • senfiaj  6 hours ago

    Yes it's "likely" to be transcendental, maybe there are some evidences that support this, but this is not a proof (keep in mind that it isn't even proven to be irrational yet). Similarly, most mathematicians/computer scientist bet that P ≠ NP, but it doesn't make it proven and no one should claim that P ≠ NP in some article just because "it's most likely to be true" (even though some empirical real life evidence supports this hypothesis). In mathematics, some things may turn out to be contrary to our intuition and experience.

    • auggierose  5 hours ago

      It comes with the explicit comment "Not proven to be transcendental, but generally believed to be by mathematicians."

      That's really all you can do, given that 3 and 4 are really famous. At this point it is therefore just not possible to write a list of the "Fifteen Most Famous Transcendental Numbers", because this is quite possibly a different list than "Fifteen Most Famous Numbers that are known to be transcendental".

      3 replies →

  • loloquwowndueo  8 hours ago

    So it’s like “15 oldest actors to win an Oscar” and including someone who’s nominated this year but hasn’t actually won. But he might, right?

    No, my dudes. Just no. If it’s not proven transcendental, it’s not to be considered such.