Zillion Notation

This is an article which refers to a personal web site as the first source of the notion in the title. Please be careful as a personal web site is not usually a peer-reviewed source unlike academic journals, and hence might include wrong information. For more details, see this document.

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.^[1]^[2] 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,^[3] 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[]

↑ CompactStar. Zillion Notation. Retrieved May 16, 2022.
↑ CompactStar. Zillion Notation. Retrieved Jul 23, 2022.
↑ The first version of this article.

See also[]

Jonathan Bowers' -illion s

Main -illions

Tier 2: millillion* · myr · micr · nan · pic · femt · att · zept · yoct · ront · quect · mec · duec · trec · tetrec · pentec · hexec · heptec · octec · ennec · icos · meicos · dueicos · trioicos · tetreicos · penteicos · hexeicos · hepteicos · octeicos · enneicos · triacont · tetracont · pentacont · hexacont · heptacont · octacont · ennacont · hect
Tier 3: killillion · meg · gig · ter · pet · ex · zett · yott · ronn · quett · hend · dok · tradak · tedak · pedak · exdak · zedak · yodak · nedak · ik · iken · icod · ictr · icter · icpet · ikect · iczet · ikyot · icron · trak · tek · pek · exak · zak · yok · nek · hot · bot · trot · tot · pot · exot · zot · yoot · not
Tier 4: kalillion · dal · tral · tal · pal · exal · zal · yal · nal · dakal · hotal · mej · dakej · hotej · gij · ast · lun · ferm · jov · sol · bet · gloc · gax · sup · vers · mult

Generalized intermediate -illions

Unofficial extensions by CompactStar beyond Bowers' system

Tier 4: met/pyr · xev/gunt · hyp/kentr · omn/onl · out/paptr · barr/hous · barral · barrej · barrij · barrast · barrun · barrerm · barrov · barrol · barret · gic · asc · luc · ferc · joc · soc · bec · cet · cekal · meet · git · aset · lut · fert · jot · sot · beet
Tier 5: unvillion · duv · et · cuv · swiv · pyrv · oiv · en · ek · ev · twyv · eket · ekcuv · ekquiv · ekswiv · ekpryv · ekoiv · eknen · lan · lanunv · landuv · lanet · lancuv · lanquiv · lanswiv · lanpryv · lanoiv · lanen · etk · cuk · quik · swik · pryk · oik · enk · evaf · duvaf · etaf · cuvaf · quivaf · swivaf · pryvaf · oivaf · envaf
Tier 6: hapaxillion · dis · tris · tetrakis · pentakis · hexakis · heptakis · octakis · enneakis · decakis · hendecakis · dodecakis · decatriakis · decatetrakis · decapentakis · decahexakis · decaheptakis · decaoctakis · decaenneakis · icosakis · icosihenakis · icosidyakis · icositryakis · icositetrakis · icosipentakis · icosihexakis · icosiheptakis · icosioctakis · icosienneakis · triacontakis · tessaracontakis · pentecontakis · hexecontakis · hebdomecontakis · ogdoecontakis · enenecontakis · hecatontakis · diacosakis · triacosakis · tetracosakis · pentacosakis · hexacosakis · heptacosakis · octacosakis · enneacosakis

Humorous extensions

Aarex Tiaokhiao's extensions in Tier 7: redillion · bittersw
Trakaplex's humorous extensions: schmitty · inphix · schmigantic (unfinished) (· helpsophiaisflirtingme (nonexistent) · schmittypleasehelpme (nonexistent)
Redstonepillager's extensions: leet
HaydenTheGoogologist2009's extensions in Tier 10: body · head · hair · face · eye · nose · ear · mouth · lip · teeth · tongu · throat · jaw · neck · shoulder · arm · elbow · hand · nail · chest · back · stomach · kne · ankle · heel · to
NigerianPidgin's extensions in Tier 10: qaq · qalp · caskisol · dicaskisol · nijicaskisol · qecask · qicask · sexicask · seqicask · ottocask · ennocask
NigerianPidgin's extensions in Tier 11: hangy · hegyek · ironikus · megmikrozz · vascor · qecask · qicask · sexicask · seqicask · gazdag · fingik · negy · rontgen · behozatal · zuhany · gyurusujj · billentyuzet · ajt · honnan · diszn · Dijillion (NigerianPidgin) · ehes · nyolcvannyolc · takar · baba · karakter · font · krim · koszonom · busz · januar · hetf · nyek · bokor · tortenelem · egyiptom · tarsashaz · tigris · pokerez · falu
XRQ CORPORATION's extensions in Tier 3: googolplex
XRQ CORPORATION's extensions in Tier 4: googolduplex
XRQ CORPORATION's extensions in Tier 5: googoltriplex
XRQ CORPORATION's extensions in Tier 6: termin · aquar · servic · spong · comb · nett · expon · adm · hecr · less · obt · playgr · check · whar · anim · grout · oreg · tront · shelf · liqu · jew · glob · ium · xiff · wemct · mibd · homr · ultim · var · squeez · tebilpictr · has · nogd · aur · trakers · icot · unth · queyn · enqu · tsun · nunt · zazt · ninj · banan · karm · guav · pizz · vist · umbrell · lav

*not Bowers'

[1] CompactStar. Zillion Notation. Retrieved May 16, 2022.

[2] CompactStar. Zillion Notation. Retrieved Jul 23, 2022.

[3] The first version of this article.

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