In an extended form of my notation
Part 0: A review of base-10
In base-10 notation, ba = 10a+b, cba = 100c+10b+a, etc, where a,b,c,etc are all digits between 0 and 9 (so no letters, punctuation, etc)
1, the multiplicative identity. Also the only natural number (not including 0) that isn't prime or composite.
2, the base of the binary number system, used in almost all modern computers and information systems.
4, the first composite number
6, the first of the series of perfect numbers, whose proper factors sum to the number itself.
9, the first odd number that is composite
11, the fifth prime and first palindromic multi-digit number in base 10.
12, the first sublime number.
17, the sum of the first 4 prime numbers, and the only prime which is the sum of 4 consecutive primes.
24, which is like 42 but different somehow
25, the first centered square number besides 1 that is also a square number.
27, the cube of 3, the value of 3^3.
28, the second perfect number.
30, the smallest sphenic number.
32, the smallest nontrivial fifth power.
36, the smallest number which is @ perfect power but not prime power.
42, the meaning of life, the universe, and everything
72, the smallest Achilles number.
496, the third perfect number.
1729, the Hardy–Ramanujan number, also known as the second taxicab number; that is, the smallest positive integer that can be written as the sum of two positive cubes in two different ways.[1]
8128, the fourth perfect number.
142857, the smallest base 10 cyclic number.
9814072356, the largest perfect power that contains no repeated digits in base ten.
Part I: The Letter notation
10^2 = 10 * 10, 10^3 = 10 * 10 * 10, etc
Normal notation: A10 = 10^10, A20= 10^20, etc
Extended notation: A(x,y) = x^y (ex. A(2,10) = 2^10 = 1024
Normal notation: B1=A1,B3=AAA1, B6 = AAAAAA1, etc
Normal notation: C1=B1,C3=BBB1, C6 = BBBBBB1, etc
Big numbers
Dialogue (A10 / B2)
Guppy (A20 / A2(10^1) / A2(A1))
Sextillion (A21)
Septillion (A24)
Octillion (A27)
Googol (A100 / AA2)
Gargoogol (A200 / A2A2)
Ogolding (A400 / A4A2)
Googolging (A500 / A5A2)
Googolchime (A1000 / AA3)
Googol bell (A5000 / A5A3)
Googoltoll (A10000 / AA4)
Guppygong (A20000 / A2A4)
Gogoltoll (A50000 / A5E4)
Googolgong (A100000 / AA5)
Centimillion (A600000 / A6A5)
Maximusmillion (A1000000 / AA6)
Goospolplex (AA7)
Guppybong (A2A7)
Gogolbong (A5A7)
Googolbong (AA8)
Maximumbillion (AA9)
Trialogue (AA10 / AAA1)
Guppybong (A2A10)
Gogolthrong (A5A10)
Googolthrong (AA11)
Maximustrillion (AA12)
Googolgandingan (AA14)
Guppyplex (AA20 / AA2A1)
Googolplex (AA50 / AA5A1)
Googolplex (AA100 / AAA2 / B(3,2)
Gargoogol-plexed (AA2A2)
Googolplexichime (AAA3)
Googolplexitoll (AAA4)
Googolplexigong (AAA5)
Millionduplex (AAA6)
Bisuperior-million (A6A6A6)
Really big numbers
Tetralogue (AAAA1 / B4)
Gogolduplex (AAA5A1)
Googolduplex (AAAA2 / B(4,2))
Googolduplexichime (AAAA3)
Googolduplexitoll (AAAA4)
Millitriplexion (AAAA6)
Pentalogue (AAAAA1 / B5)
Guppytriplex (AAAA2A1)
Googoltriplex (AAAAA2)
Googoltriplexigong (AAAAA5)
Millionquadriplex (AAAAA6)
Googoltripleximine (AAAAA8)
Hexalogue (AAAAAA1 / B6)
(Googolquadriplex) (AAAAAA2)
Guppyquadriplex ( AAAAA2A1)
Gogolquadriplex (AAAAA5A1)
Heptalogue (AAAAAAA1 / B7)
Decker/Dekalogue (B10 / BA1 / BB1 / C2)
Endekalogue (B11)
Dodekalogue (B12)
Triadekalogue (B13)
Tetradekalogue (B14)
Pentadekalogue (B15)
Hexadekalogue (B16)
Heptadekalogue (B17)
Octadekalogue (B18)
Ennadekalogue (B19)
Icosalogue (B20)
Qigfol (B25)
Triantalogue (B30)
Terantalogue (B40)
Exatalogue (B60)
Ogdatalogue (B80)
Giggol (B(100,100)/B(A2,A2))
Grangol (B(101, 2)
Bighol (B200/B2A2)
Dooqnicol (B500 / B5A2)
Chilialogue (BA3)
Myrialogue (BA4)
Giggolgong (BA5)
Chilia-chilialogue (BA6)
Chilliamyrialogue (BA7)
Myriamyrialogue (BA8)
Joycian gagol (BA9)
Dialagialogue (BA10 / BAA1 / BB2)
Extended notation: B(x,y) = AAA…(x A’s)...AAA(10,y)
Ex. B(2,3) = BB(2,3)
Giggolthrong (BA11)
Sedeniadalogue (BA16)
Guppylogue (BA20)
After around here, I can’t say these are accurate (although the above ones probably have typos and stuff as well)
Minnowlogue (BA25)
Gogologue (BA50 / BA5A1)
Googolstack (BA100 / BAA2)
Goomolduex (BA1000 / BAA3)
Goomyrolduex (BAA4)
Giggolgong (BAA5)
Googolduplexidex (BB3)
Googolplexstack (BAAA2 / BB(3,2))
Googolduplexilogue (BB(4,2))
Pentalogialogue (BB5)
Googolduplexidex (B(100, B(100, B(5,2))))
Hexalagiologue (BB6)
Heptalogialogue (BB7)
Octalogialogue (BB8) lets go Star Wars
Ennalogialogue (BB9) oh also Star Wars
Tria-Taxis (BBA1 / BBB1 / C3)
Doovolplex (BB20)
Dooqtolplex (BB25)
Doohfolplex (BB50)
Grangol (B100, 100)
Chilialogialogue (BBA3)
Myrialogialogue (BBA4)
Goodcolduex (BBAA1 / BBB2)
Sedeniadialogialogue (BBA16)
Googolstackstack (BBAA2 / BBB(2,2)
Goomolduduex (BBAA3)
Trialogialogialogue (BBB3)
Googolplexstackstack (BBAAA2 / BBB(3,2)
Googolduplexilogue (BBAAAA2 / BBB(4,2)
Tetrealogialogialogue (BBB4)
Pentalogialogialogue (BBB5)
Hexalogialogialogue (BBB6)
Heptalogialogialogue (BBB7)
Octologialogialogue (BBB8)
Ennalogialogialogue (BBB9)
(Triataxis?) (C3)
Tetrataxis (C4)
Grangoldudex B(100,10,B(100,B(100,100)))
Tetra-taxis (BBBA1 / BBBB1 / C4)
Giggolduplex (BBBA2)
Chilialogialogialogue (BBBA3)
Myrialogialogialogue (BBBA4)
(Chiliachilialogialogialogue?) (BBBA6)
(Chiliamyrialogialogialogue?) (BBBA7)
Octadialogialogialogue (BBBA8)
(Ennadialogialogialogue?) (BBBA9)
(Dekadialogialogialogue?) (BBBA10 / BBBAA1 / BBBB2 / C(4,2))
Sedeniadialogialogialogue (BBBA16)
Pentataxis (BBBBB1 / C5)
Hexataxis (C6)
Heptataxis (C7)
Octataxis (C8)
Ennataxis (C9)
Dekataxis (CA1 / CB1 / CC1 / D2)
Dodekataxis (C12)
Hecta-taxis (CA2)
Chilliataxis (CA3)
Myriataxis (CA4)
Chilliachilliataxis (CA6)
Chilliamyriataxis (CA7)
Myriamyriataxis (CA8)
Googoliataxis (CAA2)
Tetralogiataxis (CB4)
Googolduplexiataxis (CB(4,2))
Pentalogiataxis (CB5)
Hexalogiataxis (CB6)
Heptalogiataxis (CB7)
Octalogiataxis (CB8)
Ennalogiataxis (CB9)
Dekalogiataxis (CB10 / CBA1 / CBB1 / CC2 / D(2,2))
(Endekalogiataxis) (CB11)
Toomolplex (CCA3)
Gaggolduplex(CCC100)
Tria-petaxis (D3)
Tetra-petaxis (CCCC1 / D4)
Penta-petaxis (D5)
Hexa-petaxis (D6)
Hepta-petaxis (D7)
Octa-petaxis (D8)
Enna-petaxis (D9)
Deka-petaxis (D10 / DA1 / DB1… / DD1 / E2)
Tetoovol (D20 / D2D1)
Queefol (D25)
Tetrodotoxin (D30)
Heefol (D50)
Geegol (D100 / DA2)
Geegolunex (AD100)
Geegolduunex (AAD100)
Gergoltreunex (AAAD100 / B(3,D100)) (etc etc)
Geegoldecaunex (B(10,D100))
Chilliapetaxis (DA3)
Myriapetaxis (DA4)
Geegolgong (DA5)
Geegolbong (DA8)
Goodcoltetez (DAA1 / DB2)
Googolquadrex (DAA2 / DB(2,2)
Giggolquadrex (DBA2)
Gaggolquadrex (DCA2)
Tria-exaxis (E3)
Tetra-exaxis (E4)
(Penta-exaxis?) (E5)
(Hexa-exaxis?) (E6)
(Hepta-exaxis?) (E7)
(Octa-exaxis?) (E8)
(Enna-exaxis?) (E9)
(Deka-exaxis?) (E10 / EA1 / EB1… / EE1 = F2)
Gigol / Hecta-exaxis (EA2)
Chilia-exaxis (EA3)
Myria-exasis (EA4)
Chiliachilia-exaxis (EA6)
Chiliamyria-exaxis (EA7)
Giggolquinex (EBA2)
Geegolquinex (ECA2)
Gigolplex (EE100)
Tria-eptaxis (F3)
Tetra-eptaxis (F4)
(Penta-eptaxis?) (F5)
(Hexa-eptaxis?) (F6)
(Hepta-eptaxis?) (F7)
(Octa-eptaxis?) (F8)
(Enna-eptaxis?) (F9)
Deka-eptaxis (F10 / FA1 / FF1 / G1)
Goggol (FA2)
Chilia-eptaxis (FA3)
Myria-eptaxis (FA4)
(Chiliachilia-eptaxis?) (FA6)
(Chiliamyria-eptaxis?) (FA7)
Tetra-octaxis (G4)
Gagol (GA2)
Gagolplex (GG100)
Tetra-ennaxis (H4)
Googologdex (HA2)
Tetra-dekaxis (I4)
Tetra-endekaxis (J4)
Tridecal (J10)
Hdekafol (J5A1)
Googoldekex (JAA2)
Giggoldekex (JBA2)
Gaggoldekex (JCA2)
Geegoldekex (JDA2)
Gigoldekex (JEA2)
Goggoldekex (JFA2)
Gagoldekex (JGA2)
Ogdagoldekez (JHA2)
Nova gold ekes (JIA2)
Tetradodekaxis (K4)
Part II: Theta Notation
θy = (θ[y, 10])
Then, for θ[a,b],
θ[1,[z]] = A([z]), θ[3,[z]] = C([z]), etc
θ[c,d] is the c’th letter function of d
(Z can be a single value or a list of a values)
Duodekagol (LA2 / θ[12, θ[1,2]])
Tredekagol (MA2 / θ[13, θ[1,2]])
Quattordekagol (NA2 / θ[14, θ[1,2]])
Quindekegol (OA2 / θ[15, θ[1,2])
Sexdekagol (PA2 / θ[16, θ[1,2]])
Septendekagol (QA2 / θ[17, θ[1,2]])
Octadekagol (RA2 / θ[18, θ[1,2]])
Novemdekagol (SA2 / θ[19, θ[1,2]])
Icosagol (TA2 / θ[20, θ[1,2]] / θ[20, 100])
Tricontagol (θ[30, 100])
Tetracontagol (θ[40, 100])
Hoflsol (θ[50, 10] / θ50)
Pentacontagol (θ[50, 100]
BLT (θ[55, θ[1,2]])
Hexacontagol (θ[60, 100])
Heptacontagol (θ[70, 100])
Octacontagol (θ[80, 100])
Nonacontagol (θ[90, 100])
Boogol (θ[100, 10])
Gugold (θ[100, 100])
Wiggol (θ[200, 100])
Waggol (θ[300, 100])
Weegol (θ[400, 100])
Wigol (θ[500, 100])
Bwoogol (θA3)
Boogolgong (θA5)
Booilsol (θAA1 / θ(Dialogue) / θ[Dialogue, 10]
Tridecaplex (θθ10)
Great grangol (θ[θ[2, A2],A2])
Great greagol (θ[θ[3, A2],A2])
Great gigangol (θ[θ[4, A2],A2])
Great gorgegol (θ[θ[5, A2],A2])
Great gulgol (θ[θ[6, A2],A2])
Great googondol (θ[θ[10, A2],A2])
Boogolplex (θθA2)
Boogolduplex (θθθA2)
Boogoltriplex (θθθθA2)
(Boogoldekaplex) (θθθθθθθθθθθA2 / θθθθθθθθθθθθ(1,2) (12 thetas))
Part III: The Omega Notation
Ω(1)(1,x) = θA2, Ω(1)(2,x) = θθA2, etc
(Boogolhectaplex) (Ω(1)(101,A2)
Corporal (Ω(1)(99,J10) / Ω(1)(99,θ(10,10))
(Boogolchilliaplex) (Ω(1)(1001,A2)
(Boogolmyriaplex) (Ω(1)(10001,A2)
Corporalplex (Ω(1)((Ω(1)(99,J10)),J10))
And that’s as far as I’ve gotten, I have’t able to grasp 4+ unit arrays in BEAF, so nothing until then probably.