List of googolisms/Up-arrow notation level

Smaller numbers

\(f_3(10^{10^6})\) ~ \(f_4(10^{10^6})\)

 * Binary-Googolplexiduex, 2↑↑22 100
 * Zootzootplex, \(\text{googolplex}^{(\text{googolplex}-1)^{(\text{googolplex}-2)^{.^{.^{.^{4^{3^{2^1}}}}}}}}\)
 * Googolplexstack, 10↑↑1010 100
 * Googolplexidex, E100#1010 100 = E100#2#2
 * Googolplexidexiplex, E100#(1010 100 +1)
 * Megafugagoogolplex, googolplex↑↑googolplex
 * Googolplexidexiduplex, E100#(1010 100 +2)
 * Grand Kilofaxul, ~ 10↑↑1010 379
 * Zootzootduplex, \(\text{googolduplex}^{(\text{googolduplex}-1)^{(\text{googolduplex}-2)^{.^{.^{.^{4^{3^{2^{1}}}}}}}}}\)
 * Googolduplexidex, E100#1010 10 100 = E100#3#2
 * Megafugagargoogolplex, googolduplex↑↑googolduplex
 * Grand Megafaxul, ~ 10↑↑(E379#3)
 * Googoltriplexidex, E100#4#2
 * Megafugagargantugoogolplex, googoltriplex↑↑googoltriplex
 * Grand Gigafaxul, ~ 10↑↑(E379#4)
 * Googolquadriplexidex, E100#5#2
 * Grand Terafaxul, ~ 10↑↑(E379#5)
 * Googolquintiplexidex, E100#6#2
 * Grand Petafaxul, ~ 10↑↑(E379#6)
 * Binary-Doodcolplex, 2↑↑2↑↑10
 * Googolsextiplexidex, E100#7#2
 * Grand Exafaxul, ~ 10↑↑(E379#7)
 * Googolseptiplexidex, E100#8#2
 * Tria-taxis, E1#1#3 = 10↑↑10↑↑10
 * Googoloctiplexidex, E100#9#2
 * Grand Hyperillion, H*(10,2)
 * Googolnoniplexidex, E100#10#2
 * Binary-Doogolplex / Binary-Doomolplex, 2↑↑2↑↑100
 * Giggolplex, {10,giggol,2}
 * Grangoldex, E100#100#2 ~ 10↑↑10↑↑101
 * Astrabreagol, #**((10))**((10))*100
 * Kiloexpofaxul, (200!1)!1 ~ 10↑↑10↑↑198
 * Chilialogialogue, 10↑↑10↑↑1000
 * Binary-Tooqnol, 2↑↑↑5
 * Grangoldexigong, E100000#100000#2 ~ 10↑↑10↑↑100001
 * Binary-Googolduduex, 2↑↑2↑↑2100
 * Googolgoogolduplex, 10↑↑10↑↑10100
 * Ecetondudex, E303#1#3 ~ 10↑↑10↑↑10303
 * Bigrand Faxul, ~ 10↑↑10↑↑10379
 * Grand Mega / triton, 3[5], 3 in a pentagon (or circle)
 * Zootzootzootplex, \(\text{zootzootplex}^{(\text{zootzootplex}-1)^{(\text{zootzootplex}-2)^{.^{.^{.^{4^{3^{2^{1}}}}}}}}}\)
 * Bigrand Kilofaxul, ~ 10↑↑10↑↑1010 379
 * Bigrand Megafaxul, ~ 10↑↑10↑↑(E379#3)
 * Pentalogialogialogue, E1#5#3
 * Tetra-taxis, E1#1#4 = 10↑↑10↑↑10↑↑10
 * Bigrand Hyperillion, H*(10,3)
 * Googolnoniplexidudex, E100#10#3 ~ 10↑↑10↑↑10↑↑11
 * Bigrand-exi-hyperillion, H*(16,3)
 * Bigrand-icosi-hyperillion, H*(20,3)
 * Binary-Doogolduplex, 2↑↑2↑↑2↑↑100
 * Giggolduplex, {10,giggolplex,2}
 * Grangoldudex, E100#100#3 ~ 10↑↑10↑↑10↑↑101
 * Astratreagol, #**((10))**((10))**((10))*100
 * Megaexpofaxul, ((200!1)!1)!1 ~ E10#197#3
 * Grangoldudexigong, E100000#100000#3 ~ 10↑↑10↑↑10↑↑100001
 * Googolgoogoltriplex, 10↑↑10↑↑10↑↑10100
 * Ecetontridex, E303#1#4
 * Trigrand Faxul, ~ E10#(E379)#3
 * Astrantereagol, #**((10))**((10))**((10))*((10))*100
 * Trigrand Kilofaxul, ~ E10#(EE379)#3
 * Great Mega, 4[5], 4 in a pentagon (or circle)
 * Boogafive / pentro, 5↑↑↑5
 * Penta-taxis, E1#1#5 = 10↑↑↑5
 * Grangoltridex, E100#100#4
 * Astratereagol, #**((10))**((10))**((10))**((10))*100
 * Gigaexpofaxul, (((200!1)!1)!1)!1 ~ E10#197#4
 * Grangoltridexigong, E100000#100000#4
 * Ecetonquadridex, E303#1#5
 * Quadgrand Faxul, ~ E10#(E379)#4
 * Gong Mega, 5[5], 5 in a pentagon (or circle)
 * Hexa-taxis, E1#1#6 = 10↑↑↑6
 * Grangolquadridex, E100#100#5
 * Teraexpofaxul, ~ E10#197#5
 * Grangolquadridexigong, E100000#100000#5
 * Ecetonquintidex, E303#1#6
 * Quintgrand Faxul, ~ E10#(E379)#5
 * Hexomega, 6[5], 6 in a pentagon (or circle)
 * Hepta-taxis, E1#1#7 = 10↑↑↑7
 * Grangolquintidex, E100#100#6
 * Petaexpofaxul, ~ E10#197#6
 * Grangolquintidexigong, E100000#100000#6
 * Heptomega, 7[5], 7 in a pentagon (or circle)
 * Octa-taxis, E1#1#8 = 10↑↑↑8
 * Exaexpofaxul, ~ E10#197#7
 * Binary-Toodcol, 2↑↑↑10
 * Octomega, 8[5], 8 in a pentagon (or circle)
 * Enna-taxis, E1#1#9 = 10↑↑↑9
 * Googolplexioctidex, E100#2#9
 * Nonomega, 9[5], 9 in a pentagon (or circle)
 * Deka-taxis / deka-teraksys / dagcol / beeiol / toodcol / goonoltrex / tetoodol, E1#1#10 = 10↑↑↑10
 * Megiston, 10[5], 10 in a pentagon (or circle)
 * Hyperduillion, H*(10,10)
 * Qagfol, 10↑↑↑25
 * Binary-Toohfol, 2↑↑↑50
 * Binary-gaggol / Binary-Toogol, 2↑↑↑100
 * Gaggol, {10,100,3} = 10↑↑↑100
 * Greagol, E100#100#100
 * Tetrofaxul, 200!2 ~ 10↑↑↑198
 * Binary-Toomol, 2↑↑↑1000
 * Greagolgong, E100000#100000#100000
 * Binary-Googoltrex, 2↑↑↑2100
 * Googol-3-flex, 10↑↑↑10100
 * Ecetonthrex, E303#1#1#2
 * Folkman's number, 2↑↑↑2901

\(f_4(10^{10^6})\) ~ \(f_5(10^{10^6})\)

 * Binary-Googolplexitrex, 2↑↑↑22 100
 * Binary-Doogoltrex, 2↑↑↑2↑↑100
 * Grand expofaxul, ~ 10↑↑↑10↑↑198
 * A-ooga / megision, 2[6], 2 in a hexagon
 * Binary-Tetooquol, 2↑↑↑↑4
 * Grahal, g1 = 3↑↑↑↑3
 * Binary-Googolduexitrex, 2↑↑↑2↑↑2100
 * Binary-Doogolplexitrex, 2↑↑↑2↑↑2↑↑100
 * Grand kiloexpofaxul, ~ 10↑↑↑10↑↑10↑↑198
 * Grand megaexpofaxul, ~ 10↑↑↑(E10#197#3)
 * Grand gigaexpofaxul * Grand teraexpofaxul * Grand petaexpofaxul * Grand exaexpofaxul
 * Tria-petaxis, 10↑↑↑↑3
 * Binary-Toogolplex, 2↑↑↑2↑↑↑100
 * Gaggolplex, {10,gaggol,3}
 * Greagolthrex, E100#100#100#2
 * Kilotetrofaxul, (200!2)!2 ~ 10↑↑↑10↑↑↑198
 * Greagolthrexigong, E100000#100000#100000#2
 * Googolduthrex, 10↑↑↑10↑↑↑10100
 * Ecetonduthrex, E303#1#1#3
 * Bigrand expofaxul, ~ E10#10#expofaxul#2
 * Binary-Tetooqnol, 2↑↑↑↑5
 * Bigrand kiloexpofaxul, ~ E10#10#kiloexpofaxul#2
 * Grand Megisiduon / A-oogra, 3[6], 3 in a hexagon
 * Tritet, {4,4,4} = 4↑↑↑↑4
 * Bigrand megaexpofaxul, ~ E10#10#megaexpofaxul#2
 * Tetra-petaxis, 10↑↑↑↑4
 * Bigrand Hyperduillion, H*(10,10,3)
 * Binary-Toogolduplex, 2↑↑↑2↑↑↑2↑↑↑100
 * Greagolduthrex, E100#100#100#3
 * Megatetrofaxul, ((200!2)!2)!2 ~ E10#10#197#3
 * Greagolduthrexigong, E100000#100000#100000#3
 * Trigrand expofaxul, ~ E10#10#expofaxul#3
 * Trigrand kiloexpofaxul, ~ E10#10#kiloexpofaxul#3
 * Great Megisitruon / A-oogrea, 4[6], 4 in a hexagon
 * Penta-petaxis, 10↑↑↑↑5
 * Gigatetrofaxul, ~ E10#10#197#4
 * Quadgrand expofaxul, ~ E10#10#expofaxul#4
 * Gong Megisiquadruon / A-oogonga, 5[6], 5 in a hexagon
 * Boogasix / hexteto, 6↑↑↑↑6
 * Hexa-petaxis, 10↑↑↑↑6
 * Teratetrofaxul, ~ E10#10#197#5
 * Quintgrand expofaxul, ~ E10#10#expofaxul#5
 * Hexomegisiquinton / A-oohexa, 6[6], 6 in a hexagon
 * Hepta-petaxis, 10↑↑↑↑7
 * Petatetrofaxul, ~ E10#10#197#6
 * A-oohepta / Heptomegisisexton, 7[6], 7 in a hexagon
 * Octa-petaxis, 10↑↑↑↑8
 * Exatetrofaxul, ~ E10#10#197#7
 * Binary-Tetoodcol, 2↑↑↑↑10
 * A-oocta, 8[6], 8 in a hexagon
 * Enna-petaxis, 10↑↑↑↑9
 * A-ooennea, 9[6], 9 in a hexagon
 * Deka-petaxis, 10↑↑↑↑10
 * A-oomega / Megisienneaplextron, 10[6], 10 in a hexagon
 * Binary-geegol / Binary-Tetoogol, 2↑↑↑↑100
 * Geegol, {10,100,4} = 10↑↑↑↑100
 * Sexagesimal-geegol, 60↑↑↑↑100
 * Gigangol, E100#100#100#100
 * Geegolthrex, 10↑↑↑↑101
 * Geegolduthrex, 10↑↑↑↑102
 * Geegoltrethrex, 10↑↑↑↑103
 * Geegolquadruthrex, 10↑↑↑↑104
 * Geegolquinthrex, 10↑↑↑↑105
 * Geegolsexthrex, 10↑↑↑↑106
 * Geegolseptenthrex, 10↑↑↑↑107
 * Geegoloctothrex, 10↑↑↑↑108
 * Geegolnovemthrex, 10↑↑↑↑109
 * Geegoldecathrex, 10↑↑↑↑110
 * Pentofaxul, 200!3 ~ 10↑↑↑↑198
 * Binary-Tetoomol, 2↑↑↑↑1000
 * Geegolgong, 10↑↑↑↑100000
 * Gigangolgong, E100000#100000#100000#100000
 * Ecetontetrex, E303#1#1#1#2

\(f_5(10^{10^6})\) ~ \(f_6(10^{10^6})\)

 * Grand tetrofaxul, ~ 10↑↑↑↑10↑↑↑198
 * Betomega / A-oogatiplex, 2[7], 2 in a heptagon
 * Tripeno, 3↑↑↑↑↑3
 * Grand kilotetrofaxul, ~ 10↑↑↑↑10↑↑↑10↑↑↑198
 * A-oogratiplex, 3[6][6]
 * Grand megatetrofaxul, ~ 10↑↑↑↑(E10#10#197#3)
 * A-oogreatiplex, 4[6][6]
 * Grand gigatetrofaxul
 * A-oogongatiplex, 5[6][6]
 * Grand teratetrofaxul
 * A-oohexatiplex, 6[6][6]
 * Grand petatetrofaxul * Grand exatetrofaxul
 * Tria-exaxis, 10↑↑↑↑↑3
 * A-oomegatiplex, 10[6][6]
 * Geegolplex, {10,geegol,4}
 * Gigangoltetrex, E100#100#100#100#2
 * Kilopentofaxul, (200!3)!3 ~ 10↑↑↑↑10↑↑↑↑198
 * Gigangoltetrexigong, E100000#100000#100000#100000#2
 * Ecetondutetrex, E303#1#1#1#3
 * Bigrand tetrofaxul, ~ E10#10#tetrofaxul#2
 * A-oogatiduplex, 2[6][6][6]
 * Bigrand kilotetrofaxul, ~ E10#10#kilotetrofaxul#2
 * Betogiga / A-oogratiduplex, 3[7], 3 in a heptagon
 * Bigrand megatetrofaxul, ~ E10#10#megatetrofaxul#2
 * A-oogreatiduplex, 4[6][6][6]
 * A-oogongatiduplex, 5[6][6][6]
 * A-oohexatiduplex, 6[6][6][6]
 * Tetra-exaxis, 10↑↑↑↑↑4
 * A-oomegatiduplex, 10[6][6][6]
 * Gigangoldutetrex, E100#100#100#100#3
 * Megapentofaxul, ((200!3)!3)!3 ~ E10#10#10#197#3
 * Gigangoldutetrexigong, E100000#100000#100000#100000#3
 * Trigrand tetrofaxul, ~ E10#10#tetrofaxul#3
 * A-oogatitriplex, 2[6][6][6][6]
 * Trigrand kilotetrofaxul, ~ E10#10#kilotetrofaxul#3
 * A-oogratitriplex, 3[6][6][6][6]
 * Betotera / A-oogreatitriplex, 4[7], 4 in a heptagon
 * Tripent, {5,5,5} = 5↑↑↑↑↑5
 * A-oogongatitriplex, 5[6][6][6][6]
 * A-oohexatitriplex, 6[6][6][6][6]
 * A-oomegatitriplex, 10[6][6][6][6]
 * Gigapentofaxul, ~ E10#10#10#197#4
 * Quadgrand tetrofaxul, ~ E10#10#tetrofaxul#4
 * A-oogatiquadruplex, 2[6][6][6][6][6]
 * A-oogratiquadruplex, 3[6][6][6][6][6]
 * A-oogreatiquadruplex, 4[6][6][6][6][6]
 * Betopeta / A-oogongatiquadruplex, 5[7], 5 in a heptagon
 * A-oohexatiquadruplex, 6[6][6][6][6][6]
 * A-oomegatiquadruplex, 10[6][6][6][6][6]
 * Quintgrand tetrofaxul, ~ E10#10#tetrofaxul#5
 * A-oogatiquintiplex, 2[6][6][6][6][6][6]
 * A-oogratiquintiplex, 3[6][6][6][6][6][6]
 * A-oogreatiquintiplex, 4[6][6][6][6][6][6]
 * A-oogongatiquintiplex, 5[6][6][6][6][6][6]
 * Betoexa / A-oohexatiquintiplex, 6[7], 6 in a heptagon
 * Boogaseven, 7↑↑↑↑↑7
 * Betozetta / A-ooheptatisextiplex, 7[7], 7 in a heptagon
 * Betoyotta, 8[7], 8 in a heptagon
 * Betoxota, 9[7], 9 in a heptagon
 * Deka-exaxis, 10↑↑↑↑↑10
 * Betodaka / A-oomegatienneaplex, 10[7], 10 in a heptagon
 * Gigol, {10,100,5} = 10↑↑↑↑↑100
 * Gorgegol, E100#100#100#100#100
 * Hexofaxul, 200!4 ~ 10↑↑↑↑↑198
 * Gorgegolgong, E100000#100000#100000#100000#100000
 * Ecetonpentex, E303#1#1#1#1#2

\(f_6(10^{10^6})\) ~ \(f_{10}(10^{10^6})\)

 * Grand pentofaxul, ~ 10↑↑↑↑↑10↑↑↑↑198
 * Flexinega / brantomega, 2[8], 2 in a octagon
 * Grand kilopentofaxul, ~ 10↑↑↑↑↑10↑↑↑↑10↑↑↑↑198
 * Brantogiga, 3[7][7]
 * Grand megapentofaxul, ~ 10↑↑↑↑↑(E10#10#10#197#3)
 * Brantotera, 4[7][7]
 * Grand gigapentofaxul, ~ 10↑↑↑↑↑(E10#10#10#197#4)
 * Brantopeta, 5[7][7]
 * Brantoexa, 6[7][7]
 * Tria-eptaxis, 10↑↑↑↑↑10↑↑↑↑↑10
 * Gigolplex, {10,gigol,5}
 * Gorgegolpentex, E100#100#100#100#100#2
 * Kilohexofaxul, (200!4)!4 ~ 10↑↑↑↑↑10↑↑↑↑↑198
 * Gorgegolpentexigong, E100000#100000#100000#100000#100000#2
 * Ecetondupentex, E303#1#1#1#1#3
 * Bigrand pentofaxul, ~ E10#10#10#pentofaxul#2
 * Breatomega, 2[7][7][7]
 * Tethexo, 4 4
 * Breatotera, 4[7][7][7]
 * Breatopeta, 5[7][7][7]
 * Breatoexa, 6[7][7][7]
 * Tetra-eptaxis, 10 4
 * Gorgegoldupentex, E100#100#100#100#100#3
 * Megahexofaxul, ((200!4)!4)!4 ~ E10#10#10#10#197#3
 * Gorgegoldupentexigong, E100000#100000#100000#100000#100000#3
 * Trigrand pentofaxul, ~ E10#10#10#pentofaxul#3
 * Bigiatomega, 2[7][7][7][7]
 * Bigiatogiga, 3[7][7][7][7]
 * Bigatopeta, 5[7][7][7][7]
 * Bigatoexa, 6[7][7][7][7]
 * Gigahexofaxul, ~ E10#10#10#10#197#4
 * Biquadriatomega, 2[7][7][7][7][7]
 * Biquadriatogiga, 3[7][7][7][7][7]
 * Biquadriatotera, 4[7][7][7][7][7]
 * Biquadriatoexa, 6[7][7][7][7][7]
 * Biquintiatomega, 2[7][7][7][7][7][7]
 * Biquintiatogiga, 3[7][7][7][7][7][7]
 * Biquintiatotera, 4[7][7][7][7][7][7]
 * Biquintiatopeta, 5[7][7][7][7][7][7]
 * Boogaeight, 8↑↑↑↑↑↑8
 * Deka-eptaxis, 10 10
 * Goggol, {10,100,6} = 10 100
 * Gulgol, E100#100#100#100#100#100 = E100##6
 * Gulgolgong, E100000##6
 * Ecetonhex, E303#1#1#1#1#1#2
 * Grand hexofaxul, ~ 10 10↑↑↑↑↑198
 * Grand kilohexofaxul, ~ 10 10↑↑↑↑↑10↑↑↑↑↑198
 * Grand megahexofaxul, ~ 10 (E10#10#10#10#197#3)
 * Grand gigahexofaxul, ~ 10 (E10#10#10#10#197#4)
 * Tria-octaxis, 10 10 10
 * Goggolplex, {10,goggol,6}
 * Gulgolhex, E100#100#100#100#100#100#2
 * Ecetonduhex, E303#1#1#1#1#1#3
 * Gulgolhexigong
 * Bigrand hexofaxul, ~ E10#10#10#10#hexofaxul#2
 * Tetra-octaxis, 10 4
 * Gulgolduhex, E100#100#100#100#100#100#3
 * Gulgolduhexigong
 * Trigrand hexofaxul, ~ E10#10#10#10#hexofaxul#3
 * Trisept, {7,7,7} = 7 7
 * Booganine, 9 9
 * Deka-octaxis, 10 10
 * Geiggeil, (3 50) 50
 * Gagol, {10,100,7} = 10 100
 * Gaspgol, E100#100#100#100#100#100#100 = E100##7
 * Geiggeim, (3 1000) 1000
 * Gaspgolgong, E100000##7
 * Ecetonheptex, E303#1#1#1#1#1#1#2
 * Tria-ennaxis, 10 10 10
 * Gagolplex, {10,gagol,7}
 * Gaspgolheptex, E100#100#100#100#100#100#100#2
 * Gaspgolheptexigong
 * Ecetonduheptex, E303#1#1#1#1#1#1#3
 * Tetra-ennaxis, 10 4
 * Gaspgolduheptex, E100#100#100#100#100#100#100#3
 * Gaspgolduheptexigong
 * Deka-ennaxis, 10 10
 * Hecta-ennaxis, 10 100
 * Ginorgol, E100#100#100#100#100#100#100#100 = E100##8
 * Ginorgolgong, E100000##8
 * Ecetonoctex, E303#1#1#1#1#1#1#1#2
 * Tria-dekaxis, 10 10 10
 * Ginorgoloctex, E100#100#100#100#100#100#100#100#2
 * Ginorgoloctexigong
 * Ecetonduoctex, E303#1#1#1#1#1#1#1#3
 * Tetra-dekaxis, 10 4
 * Ginorgolduoctex, E100#100#100#100#100#100#100#100#3
 * Ginorgolduoctexigong
 * Deka-dekaxis, 10 10
 * Hecta-dekaxis, 10 100
 * Gargantuul, E100##9
 * Gargantuulchime, E1000##9

\(f_{10}(10^{10^6})\) ~ \(f_{\omega}(10^{10^6})\)

 * Tridecal, {10,10,10}
 * Googondol, E100##10
 * Bunalum, f12(10)
 * Googoadol, E100##11
 * Goograndol, E100##12
 * Googreadol, E100##13
 * Googigandol, E100##14
 * Googorgedol, E100##15
 * Googuldol, E100##16
 * Googaspdol, E100##17
 * Googinordol, E100##18
 * Googarganduul, E100##19
 * Googonkosol, E100##20
 * Bibalum, f22(10)
 * Googontritol, E100##30
 * Bitralum, f32(10)
 * Googonsartol, E100##40
 * Biquadralum, f42(10)
 * Googonpetol, E100##50
 * Biquintalum, f52(10)
 * Hexacontagol, {10,100,60}
 * Googonextol, E100##60
 * Bisextalum, f62(10)
 * Septisextalum, f67(10)
 * Googoneptol, E100##70
 * Biseptalum, f72(10)
 * Octiseptalum, f78(10)
 * Octacontagol, {10,100,80}
 * Googonogdol, E100##80
 * Boctalum, f82(10)
 * Googonentol, E100##90
 * Binonalum, f92(10)
 * Boogahundred, {100,100,98}
 * Boogol / kiloogol, {10,10,100}
 * Woogol, hyper(10,102,100) = {10,100,100}
 * Gugold, E100##100
 * Astragold, #^((10))*100
 * Wiggol, {10,100,200}
 * Hyperfaxul, 200![1] = 200!200 ~ {10,198,201}
 * Waggol, {10,100,300}
 * Weegol, {10,100,400}
 * Wigol, {10,100,500}
 * Woggol, {10,100,600}
 * Wagol, {10,100,700}
 * Bwoogol, {10,10,1000}
 * Boogolgong, {10,10,100000}
 * Gugoldagong, E100000##100000
 * Boogagoogol, {10100,10100,10100-2}
 * Gongol, hyper(10,10100,100) = {10,100,10100}
 * Googoldiflux, 10↑(10 100) (10100)

Larger numbers