Base Pi Hyper-Operations Catullus Fellow Posts: 213 Threads: 47 Joined: Jun 2022   06/24/2022, 06:49 AM (This post was last modified: 11/08/2022, 06:06 AM by Catullus.) What properties do hyperoperations base pi have? π+π~6.283. π*π~9.870. π^π~36.462. π^^π~19,924,084,821,713,599,984,983,799,892,180,468,936,939.296. For $n\in\Bbb N$, is π[n]π ever an integer/rational/constructible number/algebraic? Like before: Quote:The .png file attached to this post is smaller than the .txt file attached to this. The .txt file attached might not look right on a smart phone. The text graphs need a monospaced font. The image attached to this post looks blurry, because of the size of the image. . Also, the picture is 443 pixels by 314 pixels wide. Using logarithmic semi-operators base the pith root of pi, π{x}π For some reason, any non real valuedness is not showing up. Isn't the analytic continuation of the Kneser method not real valued at the pith root of pi? Although, I do have some issues with tetration at base the pith root of pi. Using logarithmic semi-operators base the pith root of pi, here is graph of $y=\Re(\pi\{x\}\pi)$, from $-\pi$ to $\pi$: Attached Files Thumbnail(s)       Y=Real(π{x}π).txt (Size: 1.71 KB / Downloads: 53) Please remember to stay hydrated. ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\ JmsNxn Ultimate Fellow Posts: 1,214 Threads: 126 Joined: Dec 2010 06/24/2022, 08:41 AM Catullus, be clearer. What is this a graph of? You write $\pi[x]\pi$. What does that mean? Please work better. Explain better. Catullus Fellow Posts: 213 Threads: 47 Joined: Jun 2022 06/24/2022, 08:46 AM (This post was last modified: 11/08/2022, 06:33 AM by Catullus.) (06/24/2022, 08:41 AM)JmsNxn Wrote: Catullus, be clearer. What is this a graph of? You write $\pi[x]\pi$. What does that mean? Please work better. Explain better.It is a graph of $\def\ {\sqrt[\pi]{\pi}}\def\e{\log_\ ^{x-1}(\pi)}y=\Re(\exp_\ ^{x-1}(\e+\e))$, with the analytic continuation of the Kneser method, where x goes from $-\pi$ to $\pi$. Please remember to stay hydrated. ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\ Catullus Fellow Posts: 213 Threads: 47 Joined: Jun 2022 11/08/2022, 06:51 AM I managed to make $\def\ {\sqrt[\pi]{\pi}}\def\e{\log_\ ^{x-1}(\pi)}\def\p{\Im(\exp_\ ^{x-1}(\e+\e))}\p$ show up. Here is a graph of $y=\p$, where x goes from $-\pi$ to $\pi$: Attached Files Thumbnail(s)       Y=Imaginary(π{x}π).txt (Size: 1.71 KB / Downloads: 54) Please remember to stay hydrated. ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\ « Next Oldest | Next Newest »

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