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Schmittyillion is a number introduced as "10^310^310... a googol minus 2 more times raised to the 4182001".[1] The term was coined by Trakaplex trying to coin the largest googolism ending in "illion". It is intended to be a tier googol illion with respect to Bower's system, which has never been used, according to the creator. It was first clarified on Googology Testing Wiki[2], but the defining formula included undefined convention on brackests and was based on a misconception of the behaviour of tetration.[3] Later, it was mentioned to on a new answers.com post asking the "biggest known number in the world", but the description was ambiguous, too. Finally, the creator clarified the precise definition, as we will show in "Explanation" section. The complexity couldn't simply be written in simple notation.

Issue

It was unknown what the original definition "10^310^310... a googol minus 2 more times raised to the 4182001" precisely meant when the original definition was posted. Later, the creator explained it as \(10^{^{13}3\times10^{3,000}+3}\),[3] which is still ambiguous.

Finally, the creator explained that this number is expressed in the following way:[4]

103*103*103*103*10....(a googol of these 3*10's)4182001(back down)+3

Although it includes ellipsis, it looks clearer than the original description.

More graphic Definition

\(10^{\underbrace{3\times 10^{.^{.^{.^{3\times 10^{4182001}}}}}}_{10^{100}\quad 3\times 10's} + 3}\) This still has ellipses, but it is easier to see what is likely meant.

Alternative definition

Considering the creator's explanations, the intended value of the number is perhaps given as \(10^{a_{\textrm{googol}}+3}\) using the sequence \((a_n)_{n=1}^{\infty}\) defined in the following recursive way:

  1. If \(n = 1\), then \(a_n := 3 \times 10^{4182001}\)
  2. If \(n > 1\), then \(a_n := 3 \times 10^{a_{n-1}}\)

Etymology

It is based off 'Schmitty Winkleson' and the word 'illion'.

See also

Tier 2: millillion* · myr · micr · nan · pic · femt · att · zept · yoct · xon · vec · 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 · killamill · killamicr · killanan · killapic · killafemt · killavec · killaicos · killahect · meg · gig · ter · pet · ex · zett · yott · xenn · dak · hend · dok · tradak · tedak · pedak · exdak · zedak · yodak · nedak · ik · iken · icod · ictr · icter · icpet · ikect · iczet · ikyot · icxen · 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
Saibian's extensions in Tier 2: centimillillion · novemnon...nongent · treicos · metriacont · duetriacont · triotriacont · tetretriacont · dohect · triahect · tetrahect · pentahect · hexahect · heptahect · octahect · ennahect · enneennaconteennahect
Saibian's extensions in Tier 3: micrekill · nanekill · picekill · femtekill · attekill · zeptekill · yoctekill · xonekill · vecekill · mecekill · duecekill · icosekill · triacontekill · tetrecontekill · hectekill · exapet · enneenne...ennahect · traken · tracod · tractr · tracter · tracpet · trakect · traczet · trakyot · tracxen · teken · tecod · tectr · nonek · nonecxen
Saibian's extensions in Tier 4: hendakal · dokal · tradakal · tedakal · pedakal · exadakal · zedakal · yodakal · nedakal · ikal · total · dakij · hotij · dakast · hotast · dakun · hotun · dakerm · hoterm · dakov · hotov · dakol · hotol · daket · hotet · dakoc · hotoc · dakax · hotax · dakup · hotup · dakers · hoters · dakult · hotult · nonecxenult · nonexce...nonexcen
Nirvana's extensions in Tier 4: met · xev · hyp · omn · out · barr · barrekal · barrej · barrij · barrast · barrun · barrerm · barrov · barresol · barret · garr · aarr · lunarr · fermarr · jovarr · hut · mut
Nirvana's extensions in Tier 5: hep · ott · neat · deat · unat · ent · fit · syt · bront · geop · geopahep · geopott · geopaneat · geopadeat · geopunat · geopent · geopafit · geopasyt · geopabront · amos · amosahep · amosott · amosaneat · amosadeat · amosunat · amosent · amosafit · amosasyt · amosabront · hapr · kyr · pij · sagan · pectr · nisab · zotz · alph · bex5illion/bexllion/bexillion · gamm · delt · thet · iot · kapp · lambd · sigm
Nirvana's further extensions: Extensible Illion System numbers defined by Extensible Illion System
Trakaplex's extensions in Tier 2: · pentetriacont · metetracont · duetetracont · triotetracont · tetretetracont · pentetetracont · hexetetracont · heptetetracont · octetetracont · ennetetracont · mepentacont · duepentacont · triopentacont · tetrepentacont · pentepentacont · hexepentacont · heptepentacont · octepentacont · ennepentacont · mehexacont · dueicosedohect
Trakaplex's extensions in Tier 4: pastavec · nastihot · tunapot · nunonot · termabot · terminal · novopast · novameg · trolapet · yolopal · betabot · yetitrol · glocater · taxaperm · pekax · supanov · dupasup · pupanecter · yersosexik · yersohot · yersonastihot · multivers
Trakaplex's extensions ≥Tier 10100: schmitty · inphix · helpsophiaisflirtingme · schmigantic (unfinished)
Trakaplex's extensions ≥ Tier 10↑↑↑↑100: schmittypleasehelpme
*not Bowers'

Sources

  1. Trakaplex, a comment to "What is the biggest known number?" in Answers.com.
  2. Schmittyillion in Googology Testing Wiki.[dead link]
  3. 3.0 3.1 Trakaplex, Emphasizing Schmittyillion, Googology Wiki user blog. (The creator showed a little ambiguous expression in the blog post, and noticed a misconception in a comment.)
  4. A difference page of the talk page of this article. (The creator showed a clearer expression.)
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