Fish numbers

Fish numbers are numbers defined by the Japanese googologist Fish.Fish, Googology in Japan - exploring large numbers (2013)Fish, "Googology 2nd Edition", NextPublishing Authors Press, 2017 There are seven Fish numbers:
*Fish number 1 is an extension of the Ackermann function and is comparable to \(f_{\omega^2+1}(63)\);
*Fish number 2 is an extension of Fish number 1 and is comparable to \(f_{\omega^3}(63)\);
*Fish number 3 uses s(n) map and is comparable to \(f_{\omega^{\omega+1}\times 63+1}(63)\);
*Fish number 4 combines Fish number 3 with an oracle system;
*Fish number 5 uses a system that reaches \(\varepsilon_0\) and is comparable to \(f_{\varepsilon_0+1}(63)\);
*Fish number 6 uses an extension of that system which reaches \(\zeta_0\) and is comparable to \(f_{\zeta_0+1}(63)\);
*Fish number 7 combines Fish number 6 with an oracle system in Rayo's function.
== References ==
Fish introduced Fish number 1, Fish number 2, Fish number 3 and Fish number 5 on the publication "Mathematics SeminarFish "The world of the large number", Nippon Hyoron Sha, Vol.58, No.7, pp.28-31, 2019", and he introduced the definitions of S map and S(n) map and the relationship between the Fast-growing hierarchy and s(n) map.
Ohguro introduced Arrow notation, Chained arrow notation and the Fish numbers in the magazine "Contemporary PhilosophyT. Ohguro, "What are 'numbers' for information society?", Contemporary Philosophy, vol.47, No.15, Seidosha, 2019", and considered that the fact that Fish numbers are not a byproduct of some other goal-achieving process, but are devised purely for the generation of large numbers, is important in the gestalt change in the treatment of large numbers.
Kondo K. Kondo, "Don't there exist the large numbers no one knows how to count?", Contemporary Philosophy, vol.47, No.15, Seidosha, 2019 discussed whether large numbers that did not exist before creation can be said to have existed with Fish number 1 and Fish number 7.
== Sources ==
==See also==
ja:ふぃっしゅ数
Category:Numbers
Category:Googology in Asia
Category:Series
Category:Numbers by Fish