Coolberry's Nested bracket notation

Nested bracket notation is a notation defined by Coolberry.https://sites.google.com/view/coolberry-large-numbers/home Retrieved 2024-08-19.
== Basic Nested bracket notation ==
=== Definition ===
* Rule 1 a[] = a^a
* Rule 2 a[]b = (a[])^b
* Rule 3 a[]b[]c[]d…y[]z =(a[]b[]c[]d^…y)^z
* Rule 4 @ can be anything
* Rule 5 a[0]@ = a[]
* Rule 6 a[n] = a[n-1]a[n-1]a[n-1]a[n-1]...a[n-1]a with a copies of [n-1]
* Rule 7 a[n]b[k]c[w]..y[g]z[d] = (a[n]b[k]c[w]..y[g]^)z[d]
* Rule 7.1 a[n]...b[m]c = (a[n]...b[m])^c
=== Examples ===
* 4[] = 4^4 = 256
* 4[1]2 = (4[1])^2 = (4[0]4[0]4[0]4[0]4)^2 = (4[]4[]4[]4[]4)^2 =(256[]4[]4[]4)^2 … , according to author's calculationFirst veresion of this article. However, according to Rule 5, 4[0]4[0]4[0]4[0]4 = 4[] (where @=4[0]4[0]4[0]4) = 4^4 = 256, and then 4[1]2 = 256^2. According to Rule 3, 4[]4[]4[]4[]4 = (4[]4[]4[]4)^4 = ((4[]4[]4)^4)^4 = (((4[]4)^4)^4)^4 = ((((4[])^4)^4)^4)^4 = ((((4^4)^4)^4)^4)^4 = 4^(4*5) = 1099511627776. Therefore 4[1]2 = (4[]4[]4[]4[]4)^2 = 1099511627776^2 = 1208925819614629174706176.
* 4[2]2 = (4[2)^2 = (4[1]4[1]4[1]4[1]4)^2 =
== Sources ==
Category:Notations
Category:Functions
Category:Unformalised
Category:Numbers and functions by CoolBerry
Category:Incomplete