List of googolisms/Polynomial omega level

**List of googolisms**

* Class 0 and 1
* Class 2
* Class 3
* Class 4
* Class 5
* Tetration level
* Up-arrow notation level
* Linear omega level
* Quadratic omega level
* **Polynomial omega level**
* Exponentiated linear omega level
* Exponentiated polynomial omega level
* Double exponentiated polynomial omega level
* Triple exponentiated polynomial omega level
* Iterated Cantor normal form level
* Epsilon level
* Binary phi level
* Bachmann's collapsing level
* Higher computable level
* Uncomputable numbers

**Smaller numbers**

f

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3

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f

3

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10
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)

{\displaystyle f\_{\omega^{3}}(f\_{3}(10))}

 ~

f

ω

3

2

(

f

3

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10
)
)

## {\displaystyle f\_{\omega ^{3}2}(f\_{3}(10))}

* Choinol, s(3,2,2,1,1,2)
* Pentadecalplex, {10,3,1,1,1,2}
* Grand tetroogol, E100####100#2
* Quadroogolplex, {10,10,10,10,{10,10,10,10,100}}
* Choinolplex, s(3,3,2,1,1,2)
* Choinalbiplex, s(3,4,2,1,1,2)
* Gig-Googol, 10[1,0,0,1]100
* Tetrangol / terangol, E100####100#100
* Teris-Terribuporcal, Forcal2,1,1,2(1)
* Choinbol, s(3,2,3,1,1,2)
* Choinbolplex, s(3,3,3,1,1,2)
* Tetreagol / tereagol, E100####100#100#100
* Teris-Terribegorcal, Forcal3,1,1,2(1)
* C-tri, C(3, 3, 3)
* Tetrigangol, E100####100#100#100#100
* Tetrorgegol, E100####100##5
* Tetrulgol, E100####100##6
* Tetraspgol, E100####100##7
* Tetrinorgol, E100####100##8
* Tetrargantuul, E100####100##9
* Tetroogondol, E100####100##10
* C-decal, C(10, 10, 10)
* Tetrugold / terugold, E100####100##100
* Gig-Kiloogol, 10[0,1,0,1]100
* Booandol, 10[&2100]
* Teris-Terrible-Terribocal, Forcal1,2,1,2(1)
* Choinprimol, s(3,2,2,2,1,2)
* Choinprimolplex, s(3,3,2,2,1,2)
* Tetraatagold / teraatagold, E100####100##100#100
* Choinpribol, s(3,2,3,2,1,2)
* Choinpribolplex, s(3,3,3,2,1,2)
* Tetrugolthra / terugolthra, E100####100###3
* Teris-Terrible-Tribocal, Forcal1,3,1,2(1)
* Choinduprimol, s(3,2,2,3,1,2)
* Choinduprimolplex, s(3,3,2,3,1,2)
* Choindupribol, s(3,2,3,3,1,2)
* Choindupribolplex, s(3,3,3,3,1,2)
* Tetrugoltesla / terugoltesla, E100####100###4
* Teris-Terrible-Tetribocal, Forcal1,4,1,2(1)
* Tetrugolpeta, E100####100###5
* Tetrugolhexa, E100####100###6
* Tetrithroogol / teri-throogol, E100####100###100
* Gig-Megoogol, 10[0,0,1,1]100
* Teris-Terrible-Tris-Terribocal, Forcal1,1,2,2(1)
* Choichainol, s(3,2,2,1,2,2)
* Choichainolplex, s(3,3,2,1,2,2)
* Choichainbolplex, s(3,3,3,1,2,2)
* Choichainpribolplex, s(3,3,3,2,2,2)
* Choichaindupribolplex, s(3,3,3,3,2,2)
* Tetrithrootrigol / teri-tristo-throogol / teri-tris-throogol, E100####100###100###100
* Teris-Terrible-Tris-Tribocal, Forcal1,1,3,2(1)
* Choiduchaindupribolplex, s(3,3,3,3,3,2)
* Tetrithrootergol / teri-teristo-throogol / teri-tessi-throogol, E100####100###100###100###100
* Teris-Terrible-Tris-Tetribocal, Forcal1,1,4,2(1)
* Tetrithroopetol / teri-pesto-throogol / teri-penri-throogol, E100####100###100###100###100###100
* Tetrithroohexol / teri-existo-throogol / teri-exi-throogol, E100####100###100###100###100###100###100
* Tetrithrooheptgol, E100####100####7
* Ayaa, 1[2]0(76)
* **Tetrootrigol** / tristo-teroogol / tris-teroogol, E100####100####100 = E100#####3
* **Quadriggol** / Dugigoogol, {10,10,10,10,100,2} = 10[0,0,0,2]100

* Teris-Tribocal, Forcal1,1,1,3(1)

f

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3

2

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f

3

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10
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{\displaystyle f\_{\omega ^{3}2}(f\_{3}(10))}

## ~ **Failed to parse (Conversion error. Server ("https://services.fandom.com/mathoid-facade/") reported: "Cannot get mml. HTTP 404 Not Found"): {\displaystyle f\_{\omega ^{4}}(f\_{3}(10))}**

* Quadriggolplex, {10,10,10,10,{10,10,10,10,100,2},2}
* Tetratrithroogol / tristo-teri-throogol / tris-teri-throogol, E100####100####100###100
* Tetratrithrootrigol / tristo-teri-tristo-throogol / tris-teri-tris-throogol, E100####100####100###100###100
* Hexentri, s(3,3,3,3,3,3)
* Hexatri, {3,3,3,3,3,3}
* Ayaaa, 1[3]0(76)
* Tetrootergol / teristo-teroogol / tessi-teroogol, E100####100####100####100 = E100#####4
* Quadraggol / Trugigoogol, {10,10,10,10,100,3} = 10[0,0,0,3]100
* Quadraggolplex, {10,10,10,10,{10,10,10,10,100,3},3}
* Tri-galaxiol, #{2}{2}{2}((10))\*100
* Teris-Tetribocal, Forcal1,1,1,4(1)
* Tetraterithroogol / teristo-teri-throogol / tessi-teri-throogol, E100####100####100####100###100
* Hexentet, s(4,4,4,4,4,4)
* Hayden's Hexatri, 3(3)(3)(3)(3)3
* Ayaaaa, 1[4]0(76)
* Tetroopetol / pesto-teroogol / penri-teroogol, E100#####5
* Quadreegol, {10,10,10,10,100,4}
* Teris-Pentibocal, Forcal1,1,1,5(1)
* Hexenpent, s(5,5,5,5,5,5)
* Tetroohexol / existo-teroogol / exi-teroogol, E100#####6
* Quadrigol, {10,10,10,10,100,5}
* Hexenhex, s(6,6,6,6,6,6)
* Superhex, {6,6,6,6,6,6}
* Tetrooheptgol / episto-teroogol / epti-teroogol, E100#####7
* Quadroggol, {10,10,10,10,100,6}
* Hayden's Hexahex / hyperhex, 6(6)(6)(6)(6)6
* Tetroogogdol / ogisto-teroogol / okti-teroogol, E100#####8
* Quadragol, {10,10,10,10,100,7}
* Tetroogentol, E100#####9
* Tetroodekol, E100#####10
* Tetroogicosol, E100#####20
* **Hexadecal**, {10,10,10,10,10,10}
* Quadrexom,

f

ω

4

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10
)

{\displaystyle f\_{\omega ^{4}}(10)}
* Issou, 1[0,1]0(76)
* **Pentoogol** / pentoogith / petoogol, E100#####100
* **Quintoogol** / Teroogol (Username5243), {10,10,10,10,10,100} = 10[0,0,0,0,1]100
* Tessa-hyperon, 100{X4}100
* Cosmol, #{3}((10))\*100
* Onion-infused BEEF, {210,42,141,113,214,300}
* Petris-Terribocal, Forcal1,1,1,1,2(1)

**Failed to parse (Conversion error. Server ("https://services.fandom.com/mathoid-facade/") reported: "Cannot get mml. HTTP 404 Not Found"): {\displaystyle f\_{\omega ^{4}}(f\_{3}(10))}**
 ~

f

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ω

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f

3

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10
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## {\displaystyle f\_{\omega^{\omega}}(f\_{3}(10))}

* Hexadecalplex, {10,3,1,1,1,1,2}
* Grand pentoogol, E100#####100#2
* Quintoogolplex, {10,10,10,10,10,{10,10,10,10,10,100}}
* Pentrangol, E100#####100#100
* Trooandol, 10[&3100]
* Pentugold, E100#####100##100
* Pentithroogol, E100#####100###100
* Pentitetroogol, E100#####100####100
* Pentootrigol, E100#####100#####100
* Quintiggol / Duteroogol, {10,10,10,10,10,100,2} = 10[0,0,0,0,2]100
* Petris-Tribocal, Forcal1,1,1,1,3(1)
* Heptatri, {3,3,3,3,3,3,3}
* Pentootergol, E100#####100#####100#####100
* Quintaggol, {10,10,10,10,10,100,3}
* Petris-Tetribocal, Forcal1,1,1,1,4(1)
* Hayden's Heptatri, 3(3)(3)(3)(3)(3)3
* Pentoopetol, E100#####100#####100#####100#####100 = E100######5
* Quinteegol, {10,10,10,10,10,100,4}
* Quintigol, {10,10,10,10,10,100,5}
* Quintoggol, {10,10,10,10,10,100,6}
* Supersept, {7,7,7,7,7,7,7}
* Quintagol, {10,10,10,10,10,100,7}
* Hayden's Heptahept / hyperhept, 7(7)(7)(7)(7)(7)7
* Heptadecal, {10,10,10,10,10,10,10}
* Quintexom,

f

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5

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10
)

{\displaystyle f\_{\omega^5}(10)}
* 冬の数, s(12, 12, 1, 2, 12, 1, 2)
* Issouplex, 1[0,0,1]0(76)
* **Hexoogol** / hexoogixth / ectoogol, E100######100
* **Sextoogol** / Petoogol (Username5243), {10,10,10,10,10,10,100} = 10[0,0,0,0,0,1]100
* Peta-hyperon, 100{X5}100
* Hyperiol, #{4}((10))\*100
* Ectris-Terribocal, Forcal1,1,1,1,1,2(1)
* Grand hexoogol, E100######100#2
* Hexangol, E100######100#100
* Hexootrigol, E100######100######100
* Ectris-Tribocal, Forcal1,1,1,1,1,3(1)
* Octatri, {3,3,3,3,3,3,3,3}
* Ectris-Tetribocal, Forcal1,1,1,1,1,4(1)
* Hayden's Octatri, 3(3)(3)(3)(3)(3)(3)3
* Superoct, {8,8,8,8,8,8,8,8}
* Hyperogd, 8(8)(8)(8)(8)(8)(8)8
* Octadecal, {10,10,10,10,10,10,10,10}
* Sextexom,

f

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6

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10
)

{\displaystyle f\_{\omega ^{6}}(10)}
* Issouduplex, 1[0,0,0,1]0(76)
* Heptoogol / heptoogenth / zettoogol, E100#######100
* Septoogol / Ectoogol (Username5243), {10,10,10,10,10,10,10,100} = 10[0,0,0,0,0,0,1]100
* Ultrol, #{5}((10))\*100
* Zetris-Terribocal, Forcal1,1,1,1,1,1,2(1)
* Grand heptoogol, E100#######100#2
* Heptrangol, E100#######100#100
* Ultra-galaxiol, #{5}{2}((10))\*100
* Ultra-cosmol, #{5}{3}((10))\*100
* Ultra-hyperiol, #{5}{4}((10))\*100
* Pentooandol, 10[&5100]
* Heptootrigol, E100#######100#######100
* Bi-ultrol, #{5}{5}((10))\*100
* Ultra-hyper-cosmo-galaxi-cosmo-hyper-ultrol, #{5}{4}{3}{2}{3}{4}{5}((10))\*100
* Zetris-Tribocal, Forcal1,1,1,1,1,1,3(1)
* Enneatri, {3,3,3,3,3,3,3,3,3}
* Tri-ultrol, #{5}{5}{5}((10))\*100
* Zetris-Tetribocal, Forcal1,1,1,1,1,1,4(1)
* Hayden's Ennatri, 3(3)(3)(3)(3)(3)(3)(3)3
* Superenn, {9,9,9,9,9,9,9,9,9}
* Hyperenn, 9Template:Repeat9
* Ennadecal, {10,10,10,10,10,10,10,10,10}
* Septexom, **Failed to parse (Conversion error. Server ("https://services.fandom.com/mathoid-facade/") reported: "Cannot get mml. HTTP 404 Not Found"): {\displaystyle f\_{\omega ^{7}}(10)}**
* Issoutriplex, 1[0,0,0,0,1]0(76)
* Ogdoogol / yottoogol, E100########100
* Octoogol / Zettoogol (Username5243), {10,10,10,10,10,10,10,10,100} = 10[0,0,0,0,0,0,0,1]100
* Yotris-Terribocal, Forcal1,1,1,1,1,1,1,2(1)
* Grand ogdoogol, E100########100#2
* Ogdahepti-hexapenti-tetrithroogol / yotti-zetti-ecti-peti-teri-throogol, E100########100#######100######100#####100####100###100
* Yotris-Tribocal, Forcal1,1,1,1,1,1,1,3(1)
* Ogdatri-hexi-pentateri-tetrapetithrinortrigolthra / tristo-yotti-ecti-teristo-peti-pesto-teri-tristo-thrinorgolthra / tris-yotti-ecti-tessi-peti-penri-teri-tris-thrinorgolthra, E100########100########100######100#####100#####100#####100####100####100####100####100###100###100##100##100##8
* Decatri, {3,3,3,3,3,3,3,3,3,3}
* Yotris-Tetribocal, Forcal1,1,1,1,1,1,1,4(1)
* Hayden's Dekatri, 3(3)(3)(3)(3)(3)(3)(3)(3)3
* **Iteral** / superdecal, {10,10,10,10,10,10,10,10,10,10} = {10,10 (1) 2}
* Octexom, **Failed to parse (Conversion error. Server ("https://services.fandom.com/mathoid-facade/") reported: "Cannot get mml. HTTP 404 Not Found"): {\displaystyle f\_{\omega ^{8}}(10)}**
* Hyperdecal / hiteral, 10Template:Repeat10
* Entoogol, E100#########100
* Nonoogol / Yottoogol (Username5243), {10,10,10,10,10,10,10,10,10,100} = 10[0,0,0,0,0,0,0,0,1]100
* Grand entoogol, E100#########100#2
* Undecatri, {3,3,3,3,3,3,3,3,3,3,3}
* Nonexom, **Failed to parse (Conversion error. Server ("https://services.fandom.com/mathoid-facade/") reported: "Cannot get mml. HTTP 404 Not Found"): {\displaystyle f\_{\omega ^{9}}(10)}**
* Wun, {1111!!,11!!!,11!,11!!!!,11!!!,11111!,1,1,1,11!,11}
* Dektoogol, E100##########100
* Grand dektoogol, E100##########100#2
* Decoogol / Xennoogol, {10,10,10,10,10,10,10,10,10,10,100} = 10[0,0,0,0,0,0,0,0,0,1]100
* Dodecatri, {3,3,3,3,3,3,3,3,3,3,3,3}
* Dekexom / bitetrom, **Failed to parse (Conversion error. Server ("https://services.fandom.com/mathoid-facade/") reported: "Cannot get mml. HTTP 404 Not Found"): {\displaystyle f\_{\omega ^{10}}(10)}**
* Endektoogol, E100#^#11
* Wekoogol, 10[0,0,0,0,0,0,0,0,0,0,1]100
* pete-5.c,

≈

f

ω

11

16

(
999
)

{\displaystyle \approx f\_{\omega ^{11}}^{16}(999)}
* Dekooandol, 10[&10100]
* 秋の数, 100![9, 10, 11]
* 春の数, {3, 4, 5, 3, 4, 5, 3, 4, 5, 3, 4, 5, 3, 4, 5}
* Icosolus, E100#^#20
* pete-6.c, **Failed to parse (Conversion error. Server ("https://services.fandom.com/mathoid-facade/") reported: "Cannot get mml. HTTP 404 Not Found"): {\displaystyle \approx f\_{\omega ^{23}}(9\times 2^{9999})}**
* Ultatri, {3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3}
* Hayden's Dupertri, 3(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)(3)3
* Linel, s(3,2,2{2}2)
* Triantolus, E100#^#30
* Sarantolus, E100#^#40
* Penintolus, E100#^#50
* Okojo-stoat number,

≈

f

ω

ω

(
53
)

{\displaystyle \approx f\_{\omega ^{\omega }}(53)}
* Exintolus, E100#^#60
* Ebdomintolus, E100#^#70
* Lvapofr, 1[(2)[1]]0(76)
* Ogdontolus, E100#^#80
* Goobolspeck, {10,90 (1) 2}
* Enenintolus, E100#^#90
* Goobolcrumb, {10,95 (1) 2}
* Goobolchunk, {10,99 (1) 2}
* Ternary-goobol, {4, 100 (1) 2}
* Octal-goobol, {8, 100 (1) 2}
* Hexadecimal-goobol, {16, 100 (1) 2}
* **Goobol**, {10,100 (1) 2}
* Hay-Goobol, 10(10)(10)(10) ... (10)(10)(10)10 (98 (10)'s)
* **Godgahlah** / hectolus, E100#^#100
* Linoogol, 10[0{1}1]100
* Goobolbunch, {10,101 (1) 2}
* Centoogol, {10,10,10,10,10,...,10,10,10,10,10,100} (100 10's)
* Hektexom,

f

ω

100

(
10
)

{\displaystyle f\_{\omega ^{100}}(10)}
* Hyper-hyperon, 100{XX}100
* Titanicol / centrol, #{0:1}((10))\*100
* Goobolswarm, {10,110 (1) 2}
* Giatrixul, 200![200,200,200] ~ {10,203 (1) 2}
* Kilogiatrixul, (200![200,200,200])![200,200,200]
* Megagiatrixul, ((200![200,200,200])![200,200,200])![200,200,200]
* Gigagiatrixul, (((200![200,200,200])![200,200,200])![200,200,200])![200,200,200]
* Grand Giatrixul, 200(![200,200,200])200![200,200,200]+1
* Grand Kilogiatrixul, 200(![200,200,200])(200![200,200,200])![200,200,200]+1
* Grand Megagiatrixul, 200(![200,200,200])((200![200,200,200])![200,200,200])![200,200,200]+1
* Grand Gigagiatrixul, 200(![200,200,200])(((200![200,200,200])![200,200,200])![200,200,200])![200,200,200]+1
* Bigrand Giatrixul, 200(![200,200,200])200(![200,200,200])200![200,200,200]+1+1
* Trigrand Giatrixul, 200(![200,200,200])200(![200,200,200])200(![200,200,200])200![200,200,200]+1+1+1
* Ultratri, 3(3)(3)(3...(3)(3)(3)3 (333 (3)'s)
* Goobolding, {10,500 (1) 2}
* Goobolchime, {10,1000 (1) 2}
* Chilliatolus, E100#^#1000
* Kilexom,

f

ω

1000

(
10
)

{\displaystyle f\_{\omega ^{1000}}(10)}
* Goobolbell, {10,5000 (1) 2}
* Gooboltoll, {10,10000 (1) 2}
* Myriatolus, E100#^#10000
* Goobolgong, {10,100000 (1) 2}
* Godgahlahgong, E100000#^#100000
* Superis-Terribocal, Forcal1[2]2(1)
* Megexom,

f

ω

1000000

(
10
)

{\displaystyle f\_{\omega ^{1000000}}(10)}
* Goobolbong, {10,100000000 (1) 2}
* Gigexom,

f

ω

10

9

(
10
)

{\displaystyle f\_{\omega ^{10^{9}}}(10)}
* Goobolthrong, {10,1011 (1) 2}
* Terexom, **Failed to parse (Conversion error. Server ("https://services.fandom.com/mathoid-facade/") reported: "Cannot get mml. HTTP 404 Not Found"): {\displaystyle f\_{\omega ^{10^{12}}}(10)}**
* Goobolgandigan, {10,1014 (1) 2}
* Petexom, **Failed to parse (Conversion error. Server ("https://services.fandom.com/mathoid-facade/") reported: "Cannot get mml. HTTP 404 Not Found"): {\displaystyle f\_{\omega ^{10^{15}}}(10)}**
* Exexom,

f

ω

10

18

(
10
)

{\displaystyle f\_{\omega ^{10^{18}}}(10)}
* Zettexom, **Failed to parse (Conversion error. Server ("https://services.fandom.com/mathoid-facade/") reported: "Cannot get mml. HTTP 404 Not Found"): {\displaystyle f\_{\omega ^{10^{21}}}(10)}**
* Yottexom,

f

ω

10

24

(
10
)

{\displaystyle f\_{\omega ^{10^{24}}}(10)}
* Googahlah, E100#^#(10100)

**Larger numbers**