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+--- Thread: Base Pi Hyper-Operations (/showthread.php?tid=1548)
Base Pi Hyper-Operations - Catullus - 06/24/2022
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 \(\pi\):
RE: Hyper-Operations, Base Pi - JmsNxn - 06/24/2022
Catullus, be clearer. What is this a graph of?
You write \(\pi[x]\pi\). What does that mean? Please work better. Explain better.
RE: Hyper-Operations, Base Pi - Catullus - 06/24/2022
(06/24/2022, 08:41 AM)JmsNxn Wrote: Catullus, be clearer. What is this a graph of?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 \(\pi\).
You write \(\pi[x]\pi\). What does that mean? Please work better. Explain better.
RE: Base Pi Hyper-Operations - Catullus - 11/08/2022
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 \(\pi\):