Googolisms from Hyperfactorial Array Notation

Disclaimer: all ψ 's in this page are using Madore's ψ unless specifically said so.

below order type w

Bewilderingly Incomprehensibly Tiny Googolism (BITG), 200?(-1) (reciprocal of BIGG) (ill-defined)

and so on.

Kiloheptofaxul, (200!5)!5
Megaheptofaxul, ((200!5)!5)!5
Octofaxul, 200!6
Ennofaxul, 200!7
Decofaxul, 200!8
Undecofaxul, 200!9
Doedecofaxul, 200!10
Tredecofaxul, 200!11
Icosofaxul, 200!18
Triantofaxul, 200!28
Terantofaxul, 200!38
Perantofaxul, 200!48
Hexantofaxul, 200!58
Heptantofaxul, 200!68
Octantofaxul, 200!78
Ennantofaxul, 200!88
Hectofaxul, 200!98
Chiliofaxul, 200!998

ω - ω^ω

Dopperfaxul, 200![2]
Kilodopperfaxul, (200![2])![2]
Megadopperfaxul, ((200![2])![2])![2]
Tropperfaxul, 200![3]
Quadropperfaxul, 200![4]
Quintopperfaxul, 200![5]
Sextopperfaxul, 200[6]
Septopperfaxul, 200![7]
Oxtopperfaxul, 200![8]
Novtopperfaxul, 200![9]
Dextopperfaxul, 200![10]
Googaxul (giaxul), 200![1,2] = 200![200]
Boogaxul, 200![1,1,2] = 200![1,200]
Troogaxul, 200![1,1,1,2] = 200![1,1,200]

ω^ω - ε0

Quadroogaxul, 200![1,1,1,1,2]
Quintoogaxul, 200![1,1,1,1,1,2]

MORE NUMBERS COMING SOON

ε0 - Γ0

Giasixul, 200![200,200,200,200,200,200]
Giaseptuxul, 200![200,200,200,200,200,200,200]
Giaoctuxul, 200![200,200,200,200,200,200,200,200]
Gianonuxul, 200![200,200,200,200,200,200,200,200,200]
Giadecuxul, 200![200,200,200,200,200,200,200,200,200,200]
Marginaxul, 200![200]w/[200]
Marginabixul, 200![200]w/[200]w/[200]
Marginatrixul, 200![200]w/[200]w/[200]w/[200]
Marginaquaxul, 200![200]w/[200]w/[200]w/[200]w/[200]

MORE NUMBERS COMING SOON

Γ0 - ψ(Ω^Ω^ω)

Gammaxul, 200![200(1)2]
Inserted gammaxul, 200![[200(1)2](1)2]
Dulinserted gammaxul, 200![[[200(1)2](1)2](1)2]
Trilinserted gammaxul, 200![[[[200(1)2](1)2](1)2](1)2]
Qualinserted gammaxul, 200![[[[[200(1)2](1)2](1)2](1)2](1)2]
Gammabixul, 200![200,200(1)2]
Inserted gammabixul, 200![200,[200,200(1)2](1)2]
Dulinserted gammabixul, 200![200,[200,[200,200(1)2](1)2](1)2]
Trilinserted gammabixul, 200![200,[200,[200,[200,200(1)2](1)2](1)2](1)2]
Qualinserted gammabixul, 200![200,[200,[200,[200,[200,200(1)2](1)2](1)2](1)2](1)2]
Gammatrixul, 200![200,200,200(1)2]
Dulinserted gammatrixul, 200![200,200,[200,200,200(1)2](1)2]
Trilinserted gammatrixul, 200![200,200,[200,200,[200,200,200(1)2](1)2](1)2]
Qualinserted gammatrixul, 200![200,200,[200,200,[200,200,[200,200,200(1)2](1)2](1)2](1)2]
Gammaquaxul, 200![200,200,200,200(1)2]
Inserted gammaquaxul, 200![200,200,200,[200,200,200,200(1)2](1)2]
Dulinserted gammaquaxul, 200![200,200,200,[200,200,200,[200,200,200,200(1)2](1)2](1)2]
Trilinserted gammaquaxul, 200![200,200,200,[200,200,200,[200,200,200,[200,200,200,200(1)2](1)2](1)2](1)2]
Qualinserted gammaquaxul, 200![200,200,200,[200,200,200,[200,200,200,[200,200,200,[200,200,200,200(1)2](1)2](1)2](1)2](1)2]
Gamthraxul, 200![200(1)3]
Gamthrabixul, 200![200,200(1)3]
Gamthratrixul, 200![200,200,200(1)3]
Gamthraquaxul, 200![200,200,200,200(1)3]
Gamtetraxul, 200![200(1)4]
Gampentaxul, 200![200(1)5]
Gamhexaxul, 200![200(1)6]
Gamheptaxul, 200![200(1)7]
Gamottaxul, 200![200(1)8]
Gamentaxul, 200![200(1)9]
Gamdeckaxul, 200![200(1)10]
Hugexul, 200![200(1)200]
Giaxhugexul, 200![200,200(1)200]
Giabixhugexul, 200![200,200,200(1)200]
Giatrixhugexul, 200![200,200,200,200(1)200]
Giaquaxhugexul, 200![200,200,200,200,200(1)200]
Giaquixhugexul, 200![200,200,200,200,200,200(1)200]
Inserted hugexul, 200![200(1)[200(1)200]]
Dulinserted hugexul, 200![200(1)[200(1)[200(1)200]]]
Trilinserted hugexul, 200![200(1)[200(1)[200(1)[200(1)200]]]]
Qualinserted hugexul, 200![200(1)[200(1)[200(1)[200(1)[200(1)200]]]]]
Superior hugexul, 200![200(1)200,200]
Inserted superior hugexul, 200![200(1)200,[200(1)200,200]]
Dulinserted superior hugexul, 200![200(1)200,[200(1)200,[200(1)200,200]]]
Trilinserted superior hugexul, 200![200(1)200,[200(1)200,[200(1)200,[200(1)200,200]]]]
Qualinserted superior hugexul, 200![200(1)200,[200(1)200,[200(1)200,[200(1)200,[200(1)200,200]]]]]
Bisuperior hugexul, 200![200(1)200,200,200]
Inserted bisuperior hugexul, 200![200(1)200,200,[200(1)200,200,200]]
Dulinserted bisuperior hugexul, 200![200(1)200,200,[200(1)200,200,[200(1)200,200,200]]]
Trilinserted bisuperior hugexul, 200![200(1)200,200,[200(1)200,200,[200(1)200,200,[200(1)200,200,200]]]]
Qualinserted bisuperior hugexul, 200![200(1)200,200,[200(1)200,200,[200(1)200,200,[200(1)200,200,[200(1)200,200,200]]]]]
Trisuperior hugexul, 200![200(1)200,200,200,200]
Quadrisuperior hugexul, 200![200(1)200,200,200,200,200]
Quinsuperior hugexul, 200![200(1)200,200,200,200,200,200]
Sexasuperior hugexul, 200![200(1)200,200,200,200,200,200,200]
Septasuperior hugexul, 200![200(1)200,200,200,200,200,200,200,200]
Octasuperior hugexul, 200![200(1)200,200,200,200,200,200,200,200,200]
Nonasuperior hugexul, 200![200(1)200,200,200,200,200,200,200,200,200,200]
Decisuperior hugexul, 200![200(1)200,200,200,200,200,200,200,200,200,200,200]
Hexacthulaxul, 200![200(1)1(1)2]
Hexacthulabixul, 200![200,200(1)1(1)2]
Hexacthulatrixul, 200![200,200,200(1)1(1)2]
Hexacthulaquaxul, 200![200,200,200,200(1)1(1)2]
Secunda-hexacthulaxul, 200![200(1)200(1)2]
Bisecunda-hexacthulaxul, 200![200,200(1)200(1)2]
Trisecunda-hexacthulaxul, 200![200,200,200(1)200(1)2]
Quasecunda-hexacthulaxul, 200![200,200,200,200(1)200(1)2]
Secunda-hexacthulabixul, 200![200(1)200,200(1)2]
Secunda-hexacthulatrixul, 200![200(1)200,200,200(1)2]
Secunda-hexacthulaquaxul, 200![200(1)200,200,200,200(1)2]
Hexacthulthraxul, 200![200(1)200(1)3]
Hexacthultetraxul, 200![200(1)200(1)4]
Hugebixul, 200![200(1)200(1)200]
Giaxhugebixul, 200![200,200(1)200(1)200]
Secunda-giaxhugebixul, 200![200(1)200,200(1)200]
Secunda-giabixhugebixul, 200![200(1)200,200,200(1)200]
Secunda-giatrixhugebixul, 200![200(1)200,200,200,200(1)200]
Secunda-giaquaxhugebixul, 200![200(1)200,200,200,200,200(1)200]
Inserted hugebixul, 200![200(1)200(1)[200(1)200(1)200]]
Superior hugebixul, 200![200(1)200(1)200,200]
Inserted superior hugebixul, 200![200(1)200(1)200,[200(1)200(1)200,200]]
Bisuperior hugebixul, 200![200(1)200(1)200,200,200]
Inserted bisuperior hugebixul, 200![200(1)200(1)200,200,[200(1)200(1)200,200,200]]
Trisuperior hugebixul, 200![200(1)200(1)200,200,200,200]
Quadrisuperior hugebixul, 200![200(1)200(1)200,200,200,200,200]
Quinsuperior hugebixul, 200![200(1)200(1)200,200,200,200,200,200]
Sexasuperior hugebixul, 200![200(1)200(1)200,200,200,200,200,200,200]
Septasuperior hugebixul, 200![200(1)200(1)200,200,200,200,200,200,200,200]
Octasuperior hugebixul, 200![200(1)200(1)200,200,200,200,200,200,200,200,200]
Nonasuperior hugebixul, 200![200(1)200(1)200,200,200,200,200,200,200,200,200,200]
Decisuperior hugebixul, 200![200(1)200(1)200,200,200,200,200,200,200,200,200,200,200]
Heptacthulaxul, 200![200(1)1(1)1(1)2]
Secunda-heptacthulaxul, 200![200(1)200(1)1(1)2]
Tertia-heptacthulaxul, 200![200(1)200(1)200(1)2]
Heptacthulthraxul, 200![200(1)200(1)200(1)3]
Heptacthultetraxul, 200![200(1)200(1)200(1)4]
Hugetrixul, 200![200(1)200(1)200(1)200]
Ogdacthulaxul, 200![200(1)1(1)1(1)1(1)2]
Secunda-ogdacthulaxul, 200![200(1)200(1)2(1)2(1)2]
Tertia-ogdacthulaxul, 200![200(1)200(1)200(1)2(1)2]
Quarta-ogdacthulaxul, 200![200(1)200(1)200(1)200(1)2]
Ogdacthulthraxul, 200![200(1)200(1)200(1)200(1)3]
Ogdacthultetraxul, 200![200(1)200(1)200(1)200(1)4]
Hugequaxul, 200![200(1)200(1)200(1)200(1)200]
Ennacthulaxul, 200![200(1)1(1)1(1)1(1)1(1)2]
Hugequixul, 200![200(1)200(1)200(1)200(1)200(1)200]
Dekathulaxul, 200![200(1)1(1)1(1)1(1)1(1)1(1)2]
Godsgodgulaxul, intended to be comparable to godsgodguliterator
Enormaxul-by-hugexul, 200![200(2)200(1)200]
Enormaxul-by-superior hugexul, 200![200(2)200(1)200,200]
Enormaxul-by-bisuperior hugexul, 200![200(2)200(1)200,200,200]
Enormaxul-by-trisuperior hugexul, 200![200(2)200(1)200,200,200,200]
Enormaxul-by-quadrisuperior hugexul, 200![200(2)200(1)200,200,200,200,200]
Enormaxul-by-hugebixul, 200![200(2)200(1)200(1)200]
Enormaxul-by-hugetrixul, 200![200(2)200(1)200(1)200(1)200]
Enormaxul-by-hugequaxul, 200![200(2)200(1)200(1)200(1)200(1)200]
Enormaxul-by-hugequixul, 200![200(2)200(1)200(1)200(1)200(1)200(1)200]
Enormabixul-by-hugexul, 200![200(2)200(2)200(1)200]
Enormaquixul, 200![200(2)200(2)200(2)200(2)200(2)200]
Trenormaxul, 200![200(3)200] Cookie Fonster called this another "unnamed HAN number". Why didn't he just coin a name out of that?
Superior trenormaxul, 200![200(3)200,200]
Trenormaxul-by-hugexul, 200![200(3)200(1)200]
Trenormaxul-by-enormaxul, 200![200(3)200(2)200]
Trenormabixul, 200![200(3)200(3)200]
Trenormatrixul, 200![200(3)200(3)200(3)200]
Trenormaquaxul, 200![200(3)200(3)200(3)200(3)200]
Tetrenormaxul, 200![200(4)200]
Pentenormaxul, 200![200(5)200]
Hexenormaxul, 200![200(6)200]
Heptenormaxul, 200![200(7)200]
Octenormaxul, 200![200(8)200]
Ennenormaxul, 200![200(9)200]
Deckenormaxul, 200![200(10)200]
Destruxul, 200![200(200)200]]
John pellinger, 203![431,112(937)20,3,431(112)9,3(720)3431112937]
Grand john pellinger, 203(![431,112(937)20,3,431(112)9,3(720)3431112937])^(203![431,112(937)20,3,431(112)9,3(720)3431112937]) (^ indicate superscript and is NOT an exponent)

In general, 200![200(n)200] ≈ order type ψ(Ω^Ω^n)

ψ(Ω^Ω^ω) - ψ(Ω^Ω^Ω)

Kilosegunestruxul, (200![200([1])200])![200([1])200]
Megasegunestruxul, ((200![200([1])200])![200([1])200])![200([1])200]
Superior segunestruxul, 200![200([1])200,200]
Bisuperior segunestruxul, 200![200([1])200,200,200]
Segunestruxul-by-hugexul, 200![200([1])200(1)200]
Segunestruxul-by-enormaxul, 200![200([1])200(2)200]
Segunestruxul-by-trenormaxul, 200![200([1])200(3)200]
Great segunestruxul, 200![200([1])200([1])200]
Bigreat segunestruxul, 200![200([1])200([1])200([1])200]
Enormastruxul, 200![200([2])200]
Enormastruxul-by-destruxul, 200![200([2])200([1])200]
Great enormastruxul, 200![200([2])200([2])200]
Trenormastruxul, 200![200([3])200]
Tetrenormastruxul, 200![200([4])200]
Pentenormastruxul, 200![200([5])200]
Googastruxul, 200![200([1,2])200]
Googastrufaxul, 200![200([1,3])200]
Boogastruxul, 200![200([1,1,2])200]
Troogastruxul, 200![200([1,1,1,2])200]
Quadroogastruxul, 200![200([1,1,1,1,2])200]
Gammaastruxul, 200![200([200(1)2])200]
Hugexustruxul, 200![200([200(1)200])200]
Enormaxustruxul, 200![200([200(2)200])200]
Trenormaxustruxul, 200![200([200(3)200])200]
Segunestrubixul (destrubixul), 200![200([200([1])200])200]
Dusuperior segunestrubixul, 200![200([200([1])200,200])200]
Hugesuperior segunestrubixul, 200![200([200([1])200(1)200])200]
Enormastrubixul, 200![200([200([2])200])200]
Googastrubixul, 200![200([200([1,2])200])200]
Boogastrubixul, 200![200([200([1,1,2])200])200]
Goobolastrubixul, 200![200([200([1(1)2])200])200]
Hugexustrubixul, 200![200([200([200(1)200])200])200]
Segunestrutrixul (destrutrixul), 200![200([200([200([1])200])200])200]
Destruquaxul, 200![200([200([200([200([1])200])200])200])200]

And thus the limit of Hollom's old HAN "superdimensional" arrays is the LVO. Who knows what comes next...

beyond ψ(Ω^Ω^Ω)

I'll make those googolisms after I understand the "second-order brackets".

Also, just saying, making naive extensions of BIGG isn't going to work since order type ψ(I_w) (using Hyp cos' M ocf) is so big that any recursion applied to it is meaningless. Hollom also intends that a single use of the question mark should always be the largest googolism defined using HAN.

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