How about determining last digits of weak Graham's number, which is defined as:
\(wg(1) = 3\downarrow\downarrow\downarrow\downarrow 3\)
\(wg(n) = 3\downarrow_{wg(n-1)} 3\)
Weak G = wg(64). Ikosarakt1 (talk ^ contribs) 10:51, June 1, 2013 (UTC)
Can gather source from http://planetmath.org/node/87406? Jiawhien (talk) 13:59, June 9, 2013 (UTC)
- That is about one-sided limits. It is not related with the article we have. -- ☁ I want more clouds! ⛅ 14:08, June 9, 2013 (UTC)
where did this notation originally come from?[]
Cookiefonster (talk) 16:08, October 5, 2014 (UTC)
Ordinals with down-arrow notation[]
\[ \begin{eqnarray} a\downarrow^2b&:=&a\uparrow^2b\\ a\downarrow^31&:=&a\\ a\downarrow^3(b+1)&:=&(a\downarrow^3 b)\downarrow^2 a\\ a\downarrow^41&:=&a\\ a\downarrow^4(b+1)&:=&a\downarrow^3 (a\downarrow^4 b) \end{eqnarray} \] \[ \begin{eqnarray} \epsilon_0&=&\omega\downarrow^2\omega=\omega\downarrow^32\\ \epsilon_1&=&\epsilon_0\downarrow^2\omega\\ &=&(\omega\downarrow^32)\downarrow^2\omega =\omega\downarrow^33\\ \epsilon_m&=&\omega\downarrow^3m\\ \epsilon_\omega&=&\omega\downarrow^3\omega=\omega\downarrow^42\\ \phi(m,\omega)&=&\omega\downarrow^{m+3}2\\ \phi(\omega,\omega)&=&\omega\downarrow^{\omega}2\\ \phi(\phi(\omega,\omega),\omega)&=&\omega\downarrow^{\omega\downarrow^{\omega}2}2\\ \phi(\phi(\phi(\omega,\omega),\omega),\omega)&=&\omega\downarrow^{\omega\downarrow^{\omega\downarrow^{\omega}2}2}2\\ \end{eqnarray} \] \[ \begin{eqnarray} \Gamma_0&\approx&\lambda\alpha.(\omega\downarrow^\alpha2)^\omega(\omega) \end{eqnarray} \] Like Chris Bird? How do you feel about this?
Koteitan (talk) 13:50, March 18, 2018 (UTC)
FlippedBEAF (a.k.a. BEAF but the up-arrows are replaced by down-arrows)[]
See title. How would you notate FlippedBEAF? Probably by swapping the braces (and, for "chained-arrow notation but with down-arrows instead of up-arrows", flipping the chained-arrows). Example: guegol = ]10,10,2[ = 10⬇️⬇️10. KamafaDelgato021469 (talk) 05:16, June 22, 2018 (UTC)
Last digits[]
I found that the difficulty in finding the last digits of Steinhaus-Moser notation numbers only arises in down-arrow notation at weak heptation, since that is the first operator where we get large polyponents of weak pentation when a small base is given, which iterates a double exponential function where the base of the modular exponentiation keeps changing with each iteration. 3 vvv 3 ends in ...62673277091010930618159704003. 3 vvv 4 ends in ...30413553729060664274187755683.
3 vvvv 2 is the same as 3 vvv 3. 3 vvvv 3 ends in ...614267698886739120668332208003. 3 vvvv 4 ends in ...716914759662554567961717512003.
Allam(2^^n mod 10^6 for n >= 8) (talk) 14:15, 6 November 2020 (UTC)
Today I calculated the last 10 digits of 2 vvvvv 4 and 3 vvvvv 3, which are respectively ...7144953856 and ...0347616003. Allam(2^^n mod 10^6 for n >= 8) (talk) 17:13, 7 November 2020 (UTC)
Definition 3?[]
I believe there is a third definition on this page
https://oeis.org/wiki/Tetra-logarithms
It is similar to definition 2 but it refers to continuous inverses that can output non-integers like super-logarithm as an inverse of tetration rather than log* (ceil of super-logarithm). For example log*e(3) = 2 sloge(3) = between 1 and 2 (depends on the interpolation used)
Does this constitute a new definition or no? CompactStar (talk) 01:11, 13 October 2023 (UTC)
CompactStar (talk) 01:11, 13 October 2023 (UTC)