Zillion Notation

Zillion Notation (ZN) is a BEAF-like notation created by CompactStar (formerly Nirvana Supermind) useful for coining zillions similar to the ones of Jonathan Bowers. It is similar in concept to the Extensible Illion System by the same user, although the latter is much older and ill-defined while the creator incisted the well-definedness and removed sourced and correct descriptions related to the ill-definedness (cf. The main article of Extensible Illion System and its sources 9, 10, ... ,18).
According to the creator,The first version of this article. out of the many notations developed by the creator, it is the only well-defined one and the only one which has not been abandoned aside from Fast array notation. However, this statement is now obselete due to the recent creation of Ampersand Notation by the creator.
== Definition ==
Let @ represent any sequence of non-negative integers separated by commas.
A valid expression in ZN is of the form z(@). ZN outputs a positive integer for every valid expression, determined using this set of rules:
* z() = 0
* z(a) = 1000*a
* z(@, 0) = z(@)
* b > 0: z(a, b, @) = z(1000^a, (b-1), @)
If none of these rules apply, start the process shown below, starting from the second entry:
* If the entry is 0, then jump to the next entry.
* If the entry is not 0, then:
** Let n equal to this entry, and a equal to the first entry of the input.
** Decrease n by 1.
** Change the entry before n to a.
** Terminate the process.
== Examples ==
z(5, 2)
= z(1000^5, 1)
= z(10^15, 1)
= z(1000^(10^15), 0)
= z(10^(3*10^15), 0)
= 10^(3*10^15 + 3)
z(5, 0, 0, 1)
= z(5, 0, 5, 0)
= z(5, 0, 5)
= z(5, 5, 4)
= z(1000^5, 4, 4)
...
== Sources ==
== See also ==
Category:Notations
Category:Numbers and functions by CompactStar