Slog(x^^^2) - Printable Version +- Tetration Forum (https://tetrationforum.org) +-- Forum: Tetration and Related Topics (https://tetrationforum.org/forumdisplay.php?fid=1) +--- Forum: Mathematical and General Discussion (https://tetrationforum.org/forumdisplay.php?fid=3) +--- Thread: Slog(x^^^2) (/showthread.php?tid=1572)

Slog(x^^^2) - Catullus - 07/10/2022 How fast does  grow, with a base of slog greater than eta? RE: Slog(x^^^2) - JmsNxn - 07/10/2022 Hmmmm I was going to say this is another dumb thread, but Tommy could probably back me in saying.... polynomially? At most it grows exponentially... I honestly don't know. We don't know everything Catullus. But just by deduction: \[ \begin{align} \text{slog}(x \uparrow \uparrow 2) \le \text{slog}(x) + C + 1\\ \text{slog}(x\uparrow \uparrow x) \le \text{slog}(x) + x + C + 1\\ \end{align} \] I'd bet you can bound it by at least \(O(x^2)\). But other than that, I don't know. Don't think any one knows. If you could prove it you could probably prove something worthy of the Field's medal, lmao.