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This is my hyphen notation numbers.

Googol Regiment

Googol = 10-100

Googoluni = 10-1

Googolbi = 10-2

Googoltri = 10-3

Googoltetri = 10-4

Googolpenti = 10-5

...

Googoldeci = 10-10

Googolunideci = 10-11

...

Googolviginti = 10-20

Googoltriginti = 10-30

...

Googolcenti = 10-100 = Googol

...

Googolkila = 10-(10-3)

Googolmega = 10-(10-6)

Googolgiga = 10-(10-9)

...

Googolplex = 10-(10-100)

Googolplexiuni = 10-(10-1)

Googolplexibi = 10-(10-2)

...

Googolduplex = 10-(10-(10-100))

Googoltriplex = 10-(10-(10-(10-100)))

Googoltetriplex = 10-(10-(10-(10-(10-100))))

...

Doogol Regiment

Doogol = 10-100-2

Doogoluni = 10-1-2

Doogolbi = 10-2-2

...

Doogolplex = 10-(10-100-2)-2

Doogolduplex = 10-(10-(10-100-2)-2)-2

...

Troogol Regiment

Troogol = 10-100-3

Troogoluni = 10-1-3

Troogolbi = 10-2-3

...

Troogolplex = 10-(10-100-3)-3

...

Teroogol Regiment

Teroogol = 10-100-4

Teroogoluni = 10-1-4

Teroogolbi = 10-2-4

...

Teroogolplex = 10-(10-100-4)-4

...

Pentoogol Regiment

Pentoogol = 10-100-5

Pentoogoluni = 10-1-5

Pentoogolbi = 10-2-5

...

Pentoogolplex = 10-(10-100-5)-5

...

Hexoogol Regiment

Hexoogol = 10-100-6

Hexoogoluni = 10-1-6

Hexoogolbi = 10-2-6

...

Hexoogolplex = 10-(10-100-6)-6

...

Heptoogol Regiment

Heptoogol = 10-100-7

Heptoogoluni = 10-1-7

Heptoogolbi = 10-2-7

...

Heptoogolplex = 10-(10-100-7)-7

...

Octoogol Regiment

Octoogol = 10-100-8

Octoogoluni = 10-1-8

Octoogolbi = 10-2-8

...

Octoogolplex = 10-(10-100-8)-8

...

Ennoogol Regiment

Ennoogol = 10-100-9

Ennoogoluni = 10-1-9

Ennoogolbi = 10-2-9

...

Ennoogolplex = 10-(10-100-9)-9

... 

Dekoogol Regiment

Dekoogol = 10-100-10

Dekoogoluni = 10-1-10

Dekoogolbi = 10-2-10

...

Dekoogolplex = 10-(10-100-10)-10

... 

Gridoogol Regiment

Let stage 1 is googol, stage 2 is doogol, stage 3 is troogol,..., Gridoogol is stage 100.

Gridoogol = 10-100-100

Gridoogoluni = 10-100-1

Gridoogolbi = 10-100-2

...

Gridoogolplex = 10-100-(10-100-100)

...

To continue, we mix Gridoogol with Doogol:

Grid-doogol = 10-100-100-2

Grid-doogoluni = 10-100-1-2

Grid-doogolbi = 10-100-2-2

...

Grid-doogolplex = 10-100-(10-100-100-2)-2

...

Grid-troogol = 10-100-100-3

Grid-tetroogol = 10-100-100-4

Grid-pentoogol = 10-100-100-5

...

Cuberoogol Regiment

Cuberoogol = 10-100-100-100

Cuberoogoluni = 10-100-100-1

Cuberoogolbi = 10-100-100-2

...

Cuberoogolplex = 10-100-100-(10-100-100-100)

...

Cuber-doogol = 10-100-100-100-2

Cuber-troogol = 10-100-100-100-3

Cuber-teroogol = 10-100-100-100-4

Cuber-pentoogol = 10-100-100-100-5

...

Tesseroogol Regiment

Tesseroogol = 10-100-100-100-100

Tesseroogoluni = 10-100-100-100-1

Tesseroogolbi = 10-100-100-100-2

...

Tesseroogolplex = 10-100-100-100-(10-100-100-100-100)

...

Tesser-doogol = 10-100-100-100-100-2

Tesser-troogol = 10-100-100-100-100-3

Tesser-teroogol = 10-100-100-100-100-4

Tesser-pentoogol = 10-100-100-100-100-5

...

Penteroogol Regiment

Penteroogol = 10-100-100-100-100-100

Penteroogoluni = 10-100-100-100-100-1

Penteroogolbi = 10-100-100-100-100-2

...

Penteroogolplex = 10-100-100-100-100-(10-100-100-100-100-100)

...

Penter-doogol = 10-100-100-100-100-100-2

Penter-troogol = 10-100-100-100-100-100-3

Penter-teroogol = 10-100-100-100-100-100-4

Penter-pentoogol = 10-100-100-100-100-100-5

...

Hexeroogol Regiment

Hexeroogol = 10-100-100-100-100-100-100

Hexeroogoluni = 10-100-100-100-100-100-1

Hexeroogolbi = 10-100-100-100-100-100-2

...

Hexeroogolplex = 10-100-100-100-100-100-(10-100-100-100-100-100-100)

...

Hexer-doogol = 10-100-100-100-100-100-100-2

Hexer-troogol = 10-100-100-100-100-100-100-3

Hexer-teroogol = 10-100-100-100-100-100-100-4

Hexer-pentoogol = 10-100-100-100-100-100-100-5

...

Hepteroogol Regiment

Hepteroogol = 10-100-100-100-100-100-100-100

Hepteroogoluni = 10-100-100-100-100-100-100-1

Hepteroogolbi = 10-100-100-100-100-100-100-2

...

Hepteroogolplex = 10-100-100-100-100-100-100-(10-100-100-100-100-100-100-100)

...

Hepter-doogol = 10-100-100-100-100-100-100-100-2

Hepter-troogol = 10-100-100-100-100-100-100-100-3

Hepter-teroogol = 10-100-100-100-100-100-100-100-4

Hepter-pentoogol = 10-100-100-100-100-100-100-100-5

...

Octeroogol Regiment

Octeroogol = 10-100-100-100-100-100-100-100-100

Octeroogoluni = 10-100-100-100-100-100-100-100-1

Octeroogolbi = 10-100-100-100-100-100-100-100-2

...

Octeroogolplex = 10-100-100-100-100-100-100-100-(10-100-100-100-100-100-100-100-100)

...

Octer-doogol = 10-100-100-100-100-100-100-100-100-2

Octer-troogol = 10-100-100-100-100-100-100-100-100-3

Octer-teroogol = 10-100-100-100-100-100-100-100-100-4

Octer-pentoogol = 10-100-100-100-100-100-100-100-100-5

...

Ennteroogol Regiment

Ennteroogol = 10-100-100-100-100-100-100-100-100-100

Ennteroogoluni = 10-100-100-100-100-100-100-100-100-1

Ennteroogolbi = 10-100-100-100-100-100-100-100-100-2

...

Ennteroogolplex = 10-100-100-100-100-100-100-100-100-(10-100-100-100-100-100-100-100-100-100)

...

Ennter-doogol = 10-100-100-100-100-100-100-100-100-100-2

Ennter-troogol = 10-100-100-100-100-100-100-100-100-100-3

Ennter-teroogol = 10-100-100-100-100-100-100-100-100-100-4

Ennter-pentoogol = 10-100-100-100-100-100-100-100-100-100-5

...

Dekteroogol Regiment

Dekteroogol = 10-100-100-100-100-100-100-100-100-100-100

Dekteroogoluni = 10-100-100-100-100-100-100-100-100-100-1

Dekteroogolbi = 10-100-100-100-100-100-100-100-100-100-2

...

Dekteroogolplex = 10-100-100-100-100-100-100-100-100-100-(10-100-100-100-100-100-100-100-100-100-100)

...

Dekter-doogol = 10-100-100-100-100-100-100-100-100-100-100-2

Dekter-troogol = 10-100-100-100-100-100-100-100-100-100-100-3

Dekter-teroogol = 10-100-100-100-100-100-100-100-100-100-100-4

Dekter-pentoogol = 10-100-100-100-100-100-100-100-100-100-100-5

...

Superoogol Regiment

We have double hyphen numbers.

Superoogol = 10--100

Superoogoluni = 10--1

Superoogolbi = 10--2

...

Superoogolplex = 10--(10--100)

...

Super-doogol = 10--100-2

Super-troogol = 10--100-3

...

Super-gridoogol = 10--100-100

Super-grid-doogol = 10--100-100-2

...

Super-cuberoogol = 10--100-100-100

Super-tesseroogol = 10--100-100-100-100

...

Duperoogol/Dusuperoogol = 10--100--100

Truperoogol/Trusuperoogol = 10--100--100--100

...

Megeroogol Regiment

Megeroogol = 10---100

Megeroogoluni = 10---1

Megeroogolbi = 10---2

...

Megeroogolplex = 10---(10---100)

...

Mege-doogol = 10---100-2

Mege-troogol = 10---100-3

...

Mege-gridoogol = 10---100-100

Mege-grid-doogol = 10---100-100-2

...

Mege-cuberoogol = 10---100-100-100

Mege-tesseroogol = 10---100-100-100-100

...

Mege-superoogol = 10---100--100

Mege-super-doogol = 10---100--100-2

Mege-super-gridoogol = 10---100--100-100

Mege-duperoogol/Mege-dusuperoogol = 10---100--100--100

...

Duegeroogol/Dumegeroogol = 10---100---100

Truegeroogol/Trumegeroogol = 10---100---100---100

...

Gigeroogol Regiment

Gigeroogol = 10----100

Gige-doogol = 10----100-2

Gige-gridoogol = 10----100-100

Gige-superoogol = 10----100--100

Gige-megeroogol = 10----100---100

Dugigeroogol = 10----100----100

Trugigeroogol = 10----100----100----100

...

Tereroogol Regiment

Tereroogol = 10-----100

Tere-doogol = 10-----100-2

Tere-gridoogol = 10-----100-100

Tere-superoogol = 10-----100--100

Tere-megeroogol = 10-----100---100

Tere-gigeroogol = 10-----100----100

Dutereroogol = 10-----100-----100

Trutereroogol = 10-----100-----100-----100

...

Peteroogol Regiment

Peteroogol = 10------100

Pete-doogol = 10------100-2

Pete-gridoogol = 10------100-100

Pete-superoogol = 10------100--100

Pete-megeroogol = 10------100---100

Pete-gigeroogol = 10------100----100

Pete-tereroogol = 10------100-----100

Dupeteroogol = 10------100------100

...

Exeroogol Regiment

Exeroogol = 10-------100

Exe-doogol = 10-------100-2

Exe-gridoogol = 10-------100-100

Exe-superoogol = 10-------100--100

Exe-megeroogol = 10-------100---100

Exe-gigeroogol = 10-------100----100

Exe-tereroogol = 10-------100-----100

Exe-peteroogol = 10-------100------100

Duexeroogol = 10-------100-------100

...

Zetteroogol Regiment

Zetteroogol = 10--------100

Zette-doogol = 10--------100-2

Zette-gridoogol = 10--------100-100

Zette-superoogol = 10--------100--100

Zette-megeroogol = 10--------100---100

Zette-gigeroogol = 10--------100----100

Zette-tereroogol = 10--------100-----100

Zette-peteroogol = 10--------100------100

Zette-exeroogol = 10--------100-------100

Duzetteroogol = 10--------100--------100

...

Yotteroogol Regiment

Yotteroogol = 10---------100

Yotte-doogol = 10---------100-2

Yotte-gridoogol = 10---------100-100

Yotte-superoogol = 10---------100--100

Yotte-megeroogol = 10---------100---100

Yotte-gigeroogol = 10---------100----100

Yotte-tereroogol = 10---------100-----100

Yotte-peteroogol = 10---------100------100

Yotte-exeroogol = 10---------100-------100

Yotte-zetteroogol = 10---------100--------100

Duyotteroogol = 10---------100---------100

...

Xoneroogol Regiment

Xoneroogol = 10----------100

Xone-doogol = 10----------100-2

Xone-gridoogol = 10----------100-100

Xone-superoogol = 10----------100--100

Xone-megeroogol = 10----------100---100

Xone-gigeroogol = 10----------100----100

Xone-tereroogol = 10----------100-----100

Xone-peteroogol = 10----------100------100

Xone-exeroogol = 10----------100-------100

Xone-zetteroogol = 10----------100--------100

Xone-yotteroogol = 10----------100---------100

Duxoneroogol = 10----------100----------100

...

The largest non-canonical number that can be named in this scheme is dekuxone-dekuyotte-dekuzette-dekuexe-dekupete-dekutere-dekugige-dekumege-dekusuper-deker-dekoogol, which is equal to 10----------100----------100----------100----------100----------100----------100----------100----------100----------100----------100---------100---------100---------100---------100---------100---------100---------100---------100---------100---------100--------100--------100--------100--------100--------100--------100--------100--------100--------100--------100-------100-------100-------100-------100-------100-------100-------100-------100-------100-------100------100------100------100------100------100------100------100------100------100------100-----100-----100-----100-----100-----100-----100-----100-----100-----100-----100----100----100----100----100----100----100----100----100----100----100---100---100---100---100---100---100---100---100---100---100--100--100--100--100--100--100--100--100--100--100-100-100-100-100-100-100-100-100-100-100-10! That a huge number!

Godderoogol Regiment

Godderoogol = 10-^-100

Godder-doogol = 10-^-100-2

Godder-gridoogol = 10-^-100-100

Godder-superoogol = 10-^-100--100

Godder-megeroogol = 10-^-100---100

...

Dugodderoogol = 10-^-100-^-100

Trugodderoogol = 10-^-100-^-100-^-100

...

To continue, we append gridu:

Gridugodderoogol = 10-^--100

Gridugodder-godderoogol = 10-^--100-^-100

Dugridugodderoogol = 10-^--100-^--100

...

Cuberugodderoogol = 10-^---100

Tesserugodderoogol = 10-^----100

...

Superugodderoogol = 10-^-^-100

Gridusuperugodderoogol = 10-^-^--100

...

Duperugodderoogol = 10-^-^-^-100

...

Gridderoogol Regiment

Gridderoogol = 10-^^-100

Gridugridderoogol = 10-^^--100

Cuberugridderoogol = 10-^^---100

...

Superugridderoogol = 10-^^-^-100

Duperugridderoogol = 10-^^-^-^-100

...

Let change dugrideru into griderudu, dusuperu into superudu, etc.

Megerugridderoogol = 10-^^-^^-100

Dumegerugridderoogol = 10-^^-^^-^^-100

...

Cubidderoogol Regiment

Cubidderoogol = 10-^^^-100

Griducubidderoogol = 10-^^^--100

Superucubidderoogol = 10-^^^-^-100

Megerucubidderoogol = 10-^^^-^^-100

Gigerucubidderoogol = 10-^^^-^^^-100

...

Tesseridderoogol Regiment

Tesseridderoogol = 10-^^^^-100

Gridutesseridderoogol = 10-^^^^--100

Superutesseridderoogol = 10-^^^^-^-100

Megerutesseridderoogol = 10-^^^^-^^-100

Gigerutesseridderoogol = 10-^^^^-^^^-100

Tererutesseridderoogol = 10-^^^^-^^^^-100

...

Penteridderoogol Regiment

Penteridderoogol = 10-^^^^^-100

Gridupenteridderoogol = 10-^^^^^--100

Superupenteridderoogol = 10-^^^^^-^-100

Megerupenteridderoogol = 10-^^^^^-^^-100

Gigerupenteridderoogol = 10-^^^^^-^^^-100

Tererupenteridderoogol = 10-^^^^^-^^^^-100

Penterupenderidderoogol = 10-^^^^^-^^^^^-100

...

Hexeridderoogol Regiment

-- UNDER CONSTRUCTION --

Planned regiments

Googol-Dekoogol Regiment (done)

Gridderoogol-Dekeroogol Regiment (done)

Superoogol-Xoneroogol Regiment (done)

Godderoogol-Dekeridderoogol Regiment (in progress)

Staroogol-Apostrophoogol Regiment

Apostrophoogol-Triperatoroogol Regiment

Triperatoroogol-Gridperatoroogol

Gridperatoroogol-Googodgongulus Regiment

Googodgongulus Regiment, and not more to come soon.

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