Base Pi Hyper-Operations
#1
Question 
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)
   

.txt   Y=Real(π{x}π).txt (Size: 1.71 KB / Downloads: 439)
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ฅ(ミ⚈ ﻌ ⚈ミ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\
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Messages In This Thread
Base Pi Hyper-Operations - by Catullus - 06/24/2022, 06:49 AM
RE: Hyper-Operations, Base Pi - by JmsNxn - 06/24/2022, 08:41 AM
RE: Hyper-Operations, Base Pi - by Catullus - 06/24/2022, 08:46 AM
RE: Base Pi Hyper-Operations - by Catullus - 11/08/2022, 06:51 AM

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