Discussion of TPID 6 - Printable Version +- Tetration Forum ( https://math.eretrandre.org/tetrationforum)+-- Forum: Tetration and Related Topics ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1)+--- Forum: Mathematical and General Discussion ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3)+--- Thread: Discussion of TPID 6 ( /showthread.php?tid=526) |

Discussion of TPID 6 - JJacquelin - 10/22/2010
(10/07/2009, 12:03 AM)andydude Wrote: Conjecture I think that the conjecture is false. First, the numerical computation have to be carried out with much more precision. The solution for x in is approximately 1.44467831224667 which is higher than e^(1/e) The solution for x in is approximately 1.4446796588047 which is higher than e^(1/e) As n increases, x increasses very slowly. But, in any case, x is higher than e^(1/e) = 1.44466786100977 Second, on a more theoretical viewpoint, if x=e^(1/e), the limit of is e , for n tending to infinity. So, the limit isn't = n , as expected. RE: Limit of self-super-roots is e^1/e. TPID 6 - sheldonison - 10/22/2010
(10/22/2010, 11:27 AM)JJacquelin Wrote: ....I think that's a good starting point. For x=e^(1/e), the Another limit that I think holds is that the slog(e) gets arbitrarily large as the base approaches eta from above. Note that for these bases with B>eta, sexp(z) grows super exponentially when z gets big enough. Now lets pick 10000. Solve for base b>eta . We know there is another number n>10000, for which , because we know that super exponential growth will eventually set in, as n grows past 10000, and that . Then, for some number n>10000, . I actually have a hunch that somewhere around n=20000 or so that superexponential growth finally kicks in. I guess what I'm trying to get at is that we can probably prove that for , solving for b as n grows arbitrarily large, b approaches eta+. For each particular base b, there is another larger number, call it "m>n", for which Andrew's equation holds. . And that might be a pretty good step in proving Andrew's lemma. - Sheldon RE: Limit of self-super-roots is e^1/e. TPID 6 - nuninho1980 - 10/23/2010
(10/22/2010, 11:27 AM)JJacquelin Wrote: I think that the conjecture is false.The solution for x in is approximately 1.44467831224667 -> is not correct! but yes - x=1.44467829141456 The solution for x in is approximately 1.4446796588047 -> is not correct but yes - x=1.4446679658595034 you mistake!?!! eheheh! lool x=1.444667862058778534938 therefore, the conjecture is NOT false! I calculated the numbers corrects by program "pari/gp". RE: Discussion of TPID 6 - bo198214 - 10/24/2010
Hey guys, 1. please dont post discussion in the open problems survey! Its reserved for problems exclusively. 2. The conjecture is already proven: By me here By tommy here. I update the stati of the problems. |