Slog(x^^^2) Catullus Fellow Posts: 213 Threads: 47 Joined: Jun 2022   07/10/2022, 04:21 AM (This post was last modified: 08/14/2022, 08:58 PM by Catullus.) How fast does $\dpi{110} \text{slog}(x\uparrow\uparrow\uparrow2)$ grow, with a base of slog greater than eta? Please remember to stay hydrated. ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\ JmsNxn Ultimate Fellow Posts: 993 Threads: 117 Joined: Dec 2010 07/10/2022, 04:40 AM (This post was last modified: 07/10/2022, 04:41 AM by JmsNxn.) 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. « Next Oldest | Next Newest »

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