Embedded Files
4.3.6
Forging Structured-E Numbers
Introduction
With a formal definition for E: established we can finally forge on ahead into the great empty plain between Bowers' humungulus and golapulus. Few googolism's exist in this range and you are more likely to see a jump from LVO to BHO at this point. However there is a wealth of inbetween values here. We will be coining thousands of new googolism's in this largely unmapped and desserted gap between the large and the very large.
Ready for Level 5 ...
Forging E: Numbers
The following catalog features thousands of new numbers exclusive to ExE. These are broken up into regiments for convenience. Each regiment covers a fairly broad range of order-types.
Here is a list of all the currently established Regiments so far:
1. Googol Regiment
2. Grangol Regiment
3. Greagol Regiment
4. Gigangol Regiment
5. Gorgegol Regiment
6. Gulgol Regiment
7. Gaspgol Regiment
8. Ginorgol Regiment
9. Gargantuul Regiment
10. Googondal Regiment
11. Gugold Regiment
12. Graatagold Regiment
13. Greegold Regiment
14. Grinningold Regiment
15. Golaagold Regiment
16. Gruelohgold Regiment
17. Gaspgold Regiment
18. Ginorgold Regiment
19. Gugol-Gang Regiment
20. Throogol-Gang Regiment
21. Higher X-oogol Regiment
22. Godgahlah Regiment
23. Gridgahlah Regiment
24. Kubikahlah Regiment
25. Quarticahlah Regiment
26. Quinticahlah Regiment
27. Sexticahlah Regiment
28. Septicahlah Regiment
29. Octicahlah Regiment
30. Godgathor Regiment
31. Gralgathor Regiment
32. Thraelgathor Regiment
33. Terinngathor Regiment
34. Higher Gathor Regiment
35. Higher Tathol Regiment
36. Tethrathoth Regiment
37. Monster-Giant Regiment
38. Tethriterator Regiment
39. Tethracross Regiment
40. Tethracubor Regiment
41. Tethrateron Regiment
42. Tethrapeton Regiment
43. Tethrahexon Regiment
44. Tethrahepton Regiment
45. Tethra-ogdon Regiment
46. Tethrennon Regiment
47. Tethradekon Regiment
48. Tethratope Regiment
49. Pentacthulhum Regiment
50. Pentacthulhucross Regiment
51. Pentacthulcubor Regiment
52. Pentacthulteron Regiment
53. Pentacthulpeton Regiment
54. Pentacthulhexon Regiment
55. Pentacthulhepton Regiment
56. Pentacthul-ogdon Regiment
57. Pentacthulennon Regiment
58. Pentacthuldekon Regiment
59. Pentacthultope Regiment
60. Hexacthulhum Super Regiment
61. Heptacthulhum Super Regiment
62. Ogdacthulhum Super Regiment
63. Ennacthulhum Super Regiment
64. Dekacthulhum Super Regiment
65. Godsgodgulus Regiment
66. Blasphemorgulus Regiment
We will begin about where we left off with xE^, namely with Godsgodgulus Regiment. After that we return to the Blasphemorgulus Regiment. We will then go through a host of new regiments taking cues from our previous excursion but also adding in loads of new content.
Let's begin...
Godsgodgulus
Regiment
65TH REGIMENT
Members: 133
Revisiting the Godsgodgulus Regiment we will be using the new E: notation. This time I will be numbering the members of a regiment. We begin with the goliath:
(1) goliath = E100{#:#,10}100
(2) bogligog = E100{#:#,20}100
(3) golligog = E100{#:#,50}100
(4) godsgodgulus = E100{#:#,100}100
(5) gigantorgog = E100{#:#,500}100
(6) googolgong-carta-godsgodgulus = E100{#:#,100 000}100
(7) colossigog = E100{#:#,50 000 000 000 000 000}100
(8) googligog = E100{#:#,10100}100
(9) grangligog = E100{#:#,#}(E100#100)
(10) godgahlahgog = E100{#:#,#}(E100#^#100)
(11) tethrathothigog = E100{#:#,#}(E100#^^#100)
(12) pentacthuligog = E100{#:#,#}(E100#^^^#100)
(13) hexacthuligog = E100{#:#,#}(E100#^^^^#100)
...
(14) grand goliath = E100{#:#,#}10#2
(15) grand bogligog = E100{#:#,#}20#2
(16) grand golligog = E100{#:#,#}50#2
(17) grand godsgodgulus = E100{#:#,#}100#2
(18) grand gigantorgog = E100{#:#,#}500#2
(19) grand googolgong-carta-godsgodgulus = E100{#:#,#}100,000#2
(20) grand colossigog = E100{#:#,#}50,000,000,000,000,000#2
(21) grand googligog = E100{#:#,#}(10100)#2
(22) grand grangligog = E100{#:#,#}(E100#100)#2
(23) grand godgahlahgog = E100{#:#,#}(E100#^#100)#2
(24) grand tethrathothigog = E100{#:#,#}(E100{#:#,2}100)#2
(25) grand pentacthuligog = E100{#:#,#}(E100{#:#,3}100)#2
(26) grand hexacthuligog = E100{#:#,#}(E100{#:#,4}100)#2
...
(27) grand grand goliath = E100{#:#,#}10#3
(28) grand grand bogligog = E100{#:#,#}20#3
(29) grand grand golligog = E100{#:#,#}50#3
(30) grand grand godsgodgulus = E100{#:#,#}100#3
(31) grand grand gigantorgog = E100{#:#,#}500#3
(32) grand grand googolgong-carta-godsgodgulus = E100{#:#,#}100,000#3
(33) grand grand colossigog = E100{#:#,#}50,000,000,000,000,000#3
(34) grand grand googligog = E100{#:#,#}(10100)#3
(35) grand grand grangligog = E100{#:#,#}(E100#100)#3
(36) grand grand godgahlahgog = E100{#:#,#}(E100#^#100)#3
(37) grand grand tethrathothigog = E100{#:#,#}(E100{#:#,2}100)#3
(38) grand grand pentacthuligog = E100{#:#,#}(E100{#:#,3}100)#3
(39) grand grand hexacthuligog = E100{#:#,#}(E100{#:#,4}100)#3
...
(40) triple-grand goliath = E100{#:#,#}10#4
(41) triple-grand bogligog = E100{#:#,#}20#4
(42) triple-grand golligog = E100{#:#,#}50#4
(43) triple-grand godsgodgulus = E100{#:#,#}100#4
(44) triple-grand gigantorgog = E100{#:#,#}500#4
(45) triple-grand googolgong-carta-godsgodgulus = E100{#:#,#}100,000#4
(46) triple-grand colossigog = E100{#:#,#}50,000,000,000,000,000#4
(47) triple-grand googligog = E100{#:#,#}(10100)#4
...
(48) quadruple-grand goliath = E100{#:#,#}10#5
(49) quadruple-grand bogligog = E100{#:#,#}20#5
(50) quadruple-grand golligog = E100{#:#,#}50#5
(51) quadruple-grand godsgodgulus = E100{#:#,#}100#5
(52) quadruple-grand gigantorgog = E100{#:#,#}500#5
(53) quadruple-grand googolgong-carta-godsgodgulus = E100{#:#,#}100,000#5
(54) quadruple-grand colossigog = E100{#:#,#}50,000,000,000,000,000#5
(55) quadruple-grand googligog = E100{#:#,#}(10100)#5
...
(56) quintuple-grand goliath = E100{#:#,#}10#6
(57) quintuple-grand godsgodgulus = E100{#:#,#}100#6
(58) quintuple-grand gigantorgog = E100{#:#,#}500#6
...
(59) sextuple-grand goliath = E100{#:#,#}10#7
(60) sextuple-grand godsgodgulus = E100{#:#,#}100#7
(61) sextuple-grand gigantorgog = E100{#:#,#}500#7
...
(62) septuple-grand goliath = E100{#:#,#}10#8
(63) septuple-grand godsgodgulus = E100{#:#,#}100#8
(64) septuple-grand gigantorgog = E100{#:#,#}500#8
...
(65) octuple-grand goliath = E100{#:#,#}10#9
(66) octuple-grand godsgodgulus = E100{#:#,#}100#9
(67) octuple-grand gigantorgog = E100{#:#,#}500#9
...
(68) nonuple-grand goliath = E100{#:#,#}10#10
(69) nonuple-grand godsgodgulus = E100{#:#,#}100#10
(70) nonuple-grand gigantorgog = E100{#:#,#}500#10
...
(71) decuple-grand goliath = E100{#:#,#}10#11
(72) decuple-grand godsgodgulus = E100{#:#,#}100#11
(73) decuple-grand gigantorgog = E100{#:#,#}500#11
...
(74) undecuple-grand godsgodgulus = E100{#:#,#}100#12
(75) duodecuple-grand godsgodgulus = E100{#:#,#}100#13
(76) tredecuple-grand godsgodgulus = E100{#:#,#}100#14
(77) quattuordecuple-grand godsgodgulus = E100{#:#,#}100#15
(78) quindecuple-grand godsgodgulus = E100{#:#,#}100#16
(79) sexdecuple-grand godsgodgulus = E100{#:#,#}100#17
(80) septendecuple-grand godsgodgulus = E100{#:#,#}100#18
(81) octodecuple-grand godsgodgulus = E100{#:#,#}100#19
(82) novemdecuple-grand godsgodgulus = E100{#:#,#}100#20
(83) vigintuple-grand godsgodgulus = E100{#:#,#}100#21
(84) viginti-untuple-grand godsgodgulus = E100{#:#,#}100#22
(85) viginti-duple-grand godsgodgulus = E100{#:#,#}100#23
(86) viginti-triple-grand godsgodgulus = E100{#:#,#}100#24
(87) viginti-quadruple-grand godsgodgulus = E100{#:#,#}100#25
(88) viginti-quintuple-grand godsgodgulus = E100{#:#,#}100#26
(89) viginti-sextuple-grand godsgodgulus = E100{#:#,#}100#27
(90) viginti-septuple-grand godsgodgulus = E100{#:#,#}100#28
(91) viginti-octuple-grand godsgodgulus = E100{#:#,#}100#29
(92) viginti-nonuple-grand godsgodgulus = E100{#:#,#}100#30
(93) trigintuple-grand godsgodgulus = E100{#:#,#}100#31
...
(94) quadragintuple-grand godsgodgulus = E100{#:#,#}100#41
(95) quinquagintuple-grand godsgodgulus = E100{#:#,#}100#51
(96) sexagintuple-grand godsgodgulus = E100{#:#,#}100#61
(97) septuagintuple-grand godsgodgulus = E100{#:#,#}100#71
(98) octogintuple-grand godsgodgulus = E100{#:#,#}100#81
(99) nonigintuple-grand godsgodgulus = E100{#:#,#}100#91
(100) centuple-grand godsgodgulus = E100{#:#,#}100#101
... It is of coarse possible to create many many numbers I didn't mention on this list so far by combining the various components. In total there would be 1313 numbers generated from this sequence alone ( 13 base numbers with 101 possible configurations with "grand"). Of coarse we have only scratched the surface of Linear-E. We are going to want to move a little faster now...
(101) grangol-carta-godsgodgulus = E100{#:#,#}100#100
(102) greagol-carta-godsgodgulus = E100{#:#,#}100#100#100
(103) gigangol-carta-godsgodgulus = E100{#:#,#}100#100#100#100
(104) gorgegol-carta-godsgodgulus = E100{#:#,#}100##5
(105) gulgol-carta-godsgodgulus = E100{#:#,#}100##6
(106) gaspgol-carta-godsgodgulus = E100{#:#,#}100##7
(107) ginorgol-carta-godsgodgulus = E100{#:#,#}100##8
(108) gargantuul-carta-godsgodgulus = E100{#:#,#}100##9
(109) googondal-carta-godgodgulus = E100{#:#,#}100##10
...
(110) gugold-carta-godgulus = E100{#:#,#}100##100
(111) throogol-carta-godsgodgulus = E100{#:#,#}100###100
(112) teroogol-carta-godsgodgulus = E100{#:#,#}100####100
...
(113) godgahlah-carta-godsgodgulus = E100{#:#,#}100#^#100
(114) tethrathoth-carta-godsgodgulus = E100{#:#,#}100#^^#100
(115) tethriterator-carta-godsgodgulus = E100{#:#,#}100#^^#>#100
(116) pentacthulhum-carta-godsgodgulus = E100{#:#,#}100#^^^#100
(117) hexacthulhum-carta-godsgodgulus = E100{#:#,#}100#^^^^#100
(118) heptacthulhum-carta-godsgodgulus = E100{#:#,#}100{#:#,5}100
(119) ogdacthulhum-carta-godsgodgulus = E100{#:#,#}100{#:#,6}100
(120) ennacthulhum-carta-godsgodgulus = E100{#:#,#}100{#:#,7}100
(121) dekacthulhum-carta-godsgodgulus = E100{#:#,#}100{#:#,8}100
...
(122) goliath-carta-godsgodgulus = E100{#:#,#}100{#:#,10}100
(123) golligog-carta-godsgodgulus = E100{#:#,#}100{#:#,50}100
... Now we move on to a faster diagonalization...
(124) godstrigodgulus = E100{#:#,#}100{#:#,#}100
(125) godsteragodgulus = E100{#:#,#}100{#:#,#}100{#:#,#}100
(126) godspentagodgulus = E100{#:#,#}*#5
(127) gods-hexagodgulus =E100{#:#,#}*#6
(128) gods-heptagodgulus = E100{#:#,#}*#7
(129) gods-ogdagodgulus = E100{#:#,#}*#8
(130) gods-ennagodgulus = E100{#:#,#}*#9
(131) gods-dekagodgulus = E100{#:#,#}*#10
...
(132) gods-icosagodgulus = E100{#:#,#}*#20
... Now on to something higher...
(133) godsgodgulus-by-hyperion = E100{#:#,#}*#100
[TO BE CONTINUED]
Blasphemorgulus
Regiment
Members: 143
(1) blasphemorgulus = E100{#:#,1,2}100
(2) grand blasphemorgulus = E100{#:#,1,2}100#2
(3) grand grand blasphemorgulus = E100{#:#,1,2}100#3
...
(4) grangol-carta-blasphemorgulus = E100{#,#,1,2}100#100
(5) greagol-carta-blasphemorgulus = E100{#,#,1,2}100#100#100
...
(6) godgahlah-carta-blasphemorgulus = E100{#,#,1,2}100#^#100
(7) tethrathoth-carta-blasphemorgulus = E100{#,#,1,2}100#^^#100
(8) pentacthulhum-carta-blasphemorgulus = E100{#,#,1,2}100#^^^#100
(9) hexacthulhum-carta-blasphemorgulus = E100{#,#,1,2}100#^^^^#100
...
(10) godsgodgulus-carta-blasphemorgulus = E100{#,#,1,2}100#{100}#100
(11) ohmygosh-ohmygosh-ohmygosh-carta-blasphemorgulus
= E100{#,#,1,2}100#{#{#}#}#100
...
(12) blasphemorgulus-by-deuteron = E100{#,#,1,2}100{#,#,1,2}100
(13) blasphemorgulus-by-triton = E100{#,#,1,2}100{#,#,1,2}100{#,#,1,2}100
(14) blasphemorgulus-by-teterton
= E100{#,#,1,2}100{#,#,1,2}100{#,#,1,2}100{#,#,1,2}100
...
(15) blasphemorgulus-by-hyperion = E100{#,#,1,2}*#100
(16) blasphemorgulus-by-deuterohyperion = E100{#,#,1,2}*##100
(17) blasphemorgulus-by-tritohyperion = E100{#,#,1,2}*###100
(18) blasphemorgulus-by-tetertohyperion = E100{#,#,1,2}*####100
...
(19) blasphemorgulus-by-godgahlah = E100{#,#,1,2}*#^#100
(20) blasphemorgulus-by-tethrathoth = E100{#,#,1,2}*#^^#100
(21) blasphemorgulus-by-pentacthulhum = E100{#,#,1,2}*#^^^#100
(22) blasphemorgulus-by-hexacthulhum = E100{#,#,1,2}*#^^^^#100
...
(23) blasphemorgulus-by-godsgodgulus = E100{#,#,1,2}*#{100}#100
(24) blasphemorgulus-by-ohmygosh-ohmygosh-ohmygosh
= E100{#,#,1,2}*#{#{#}#}#100
...
(25) deutero-blasphemorgulus = E100{#,#,1,2}*{#,#,1,2}100
(26) trito-blasphemorgulus = E100{#,#,1,2}*{#,#,1,2}*{#,#,1,2}100
(27) teterto-blasphemorgulus = E100{#,#,1,2}*{#,#,1,2}*{#,#,1,2}*{#,#,1,2}100
...
(28) blasphemorgulfact = E100{#,#,1,2}^#100
(29) grideuterblasphemorgulus = E100{#,#,1,2}^##100
(30) kubicublasphemorgulus = E100{#,#,1,2}^###100
(31) quarticublasphemorgulus = E100{#,#,1,2}^####100
...
E100{#,#,1,2}^#^#100
E100{#,#,1,2}^#^#^#100
E100{#,#,1,2}^#^#^#^#100
...
(32) blasphemorgulipsotethrathoth = E100{#,#,1,2}^#^^#100
(33) blasphemorgulipsopentacthulhum = E100{#,#,1,2}^#^^^#100
(34) blasphemorgulipsohexacthulhum = E100{#,#,1,2}^#^^^^#100
...
(35) blasphemorgulipsogodsgodgulus = E100{#,#,1,2}^#{100}#100
(36) blasphemorgulipso-ohmygosh-ohmygosh-ohmygosh
= E100{#,#,1,2}^#{#{100}#}#100
...
E100{#,#,1,2}^{#,#,1,2}100
E100{#,#,1,2}^{#,#,1,2}^{#,#,1,2}100
E100{#,#,1,2}^{#,#,1,2}^{#,#,1,2}^{#,#,1,2}100
...
(37) terrible blasphemorgulus = E100{#,#,1,2}^^#100
(38) terrisquared blasphemorgulus = E100{#,#,1,2}^^##100
(39) terricubed blasphemorgulus = E100{#,#,1,2}^^###100
(40) territesserated blasphemorgulus = E100{#,#,1,2}^^####100
...
E100{#,#,1,2}^^#^#100
E100{#,#,1,2}^^#^#^#100
E100{#,#,1,2}^^#^#^#^#100
...
E100{#,#,1,2}^^#^^#100
E100{#,#,1,2}^^#^^#^^#100
E100{#,#,1,2}^^#^^#^^#^^#100
...
E100{#,#,1,2}^^#^^^#100
E100{#,#,1,2}^^#^^^^#100
...
E100{#,#,1,2}^^#{100}#100
...
E100{#,#,1,2}^^#{#{100}#}#100
...
(41) dupentated blasphemorgulus = E100{#,#,1,2}^^{#,#,1,2}100
(42) tripentated blasphemorgulus = E100{#,#,1,2}^^{#,#,1,2}^^{#,#,1,2}100
(43) quadrapentated blasphemorgulus
= E100{#,#,1,2}^^{#,#,1,2}^^{#,#,1,2}^^{#,#,1,2}100
...
(44) horrible blasphemorgulus = E100{#,#,1,2}^^^#100
(45) horrendous blasphemorgulus = E100{#,#,1,2}^^^^#100
(46) heptorrendous blasphemorgulus = E100({#,#,1,2}){5}#100
(47) ogdorrendous blasphemorgulus = E100({#,#,1,2}){6}#100
(48) ennorrendous blasphemorgulus = E100({#,#,1,2}){7}#100
(49) dekorrendous blasphemorgulus = E100({#,#,1,2}){8}#100
...
(50) goliahblasphemorgulus = E100({#,#,1,2}){10}#100
(51) golliblasphemorgulus = E100({#,#,1,2}){50}#100
(52) godsgoblasphemorgulus = E100({#,#,1,2}){100}#100
(53) ohmygosh-ohmygosh-ohmygoblasphemorgulus
= E100({#,#,1,2}){#{100}#}#100
(54) blasphemorgublasphemorgulus = E100({#,#,1,2}){{#,99,1,2}}#100
...
E100({#,#,1,2}){#}({#,#,1,2})100
...
(55) blasphemormygosh-blasphemormygosh
= E100({#,#,1,2}){{#,#,1,2}}({#,#,1,2})100
(56) blasphemormygosh-blasphemormygosh-blasphemormygosh
= E100({#,#,1,2}){({#,#,1,2}){{#,#,1,2}}({#,#,1,2})}({#,#,1,2})100
...
(57) tweilasphemorgue = E100{{#,#,1,2},100,1,2}100
(58) frielasphemorgue = E100{{{#,#,1,2},#,1,2},100,1,2}100
(59) fiorilasphemorgue = E100{{{{#,#,1,2},#,1,2},#,1,2},100,1,2}100
(60) finnasphemorgue = E100{{{{{#,#,1,2},#,1,2},#,1,2},#,1,2},100,1,2}100
(61) sexasphemorgue = E100{{{{{{#,#,1,2},#,1,2},#,1,2},#,1,2},#,1,2},100,1,2}100
(62) sjournalasphemorgue
= E100{{{{{{{#,#,1,2},#,1,2} ... },#,1,2},100,1,2}100 w/7 copies of ' 1,2 '
(63) attalasphemorgue
= E100{{{{{{{{#,#,1,2},#,1,2} ... },#,1,2},100,1,2}100 w/8 copies of ' 1,2 '
(64) neiulasphemorgue
= E100{{{{{{{{{#,#,1,2},#,1,2} ... },#,1,2},100,1,2}100 w/9 copies of ' 1,2 '
(65) tenasphemorgue
= E100{{{{{{{{{{#,#,1,2},#,1,2} ... },#,1,2},100,1,2}100 w/10 copies of ' 1,2 '
while we're at it we can go as far as...
(66) hundrelasphemorgue
= E100{{{ ... {{{#,#,1,2},#,1,2} ... },#,1,2},100,1,2}100 w/100 copies of ' 1,2 '
then...
(67) grand hundrelasphemorgue
= E100{{{ ... {{{#,#,1,2},#,1,2} ... },#,1,2},100,1,2}100
w/hundrelasphemorgue copies of ' 1,2 '
Alternatively we may write...
hundrelasphemorgue = E100{#:#,1,2>#}100
grand hundrelasphemorgue = E100{#:#,1,2>#}100#2
= E100{#:#,1,2>#}hundrelasphemorgue
... and here we go again -_-; ...
(68) grangol-carta-hundrelasphemorgue = E100{#:#,1,2>#}100#100
(69) greagol-carta-hundrelasphemorgue = E100{#:#,1,2>#}100#100#100
(70) gigangol-carta-hundrelasphemorgue = E100{#:#,1,2>#}100#100#100#100
...
(71) godgahlah-carta-hundrelasphemorgue = E100{#:#,1,2>#}100#^#100
(72) tethrathoth-carta-hundrelasphemorgue = E100{#:#,1,2>#}100#^^#100
(73) pentacthulhum-carta-hundrelasphemorgue = E100{#:#,1,2>#}100#^^^#100
(74) hexacthulhum-carta-hundrelasphemorgue = E100{#:#,1,2>#}100#^^^^#100
...
(75) godsgodgulus-carta-hundrelasphemorgue = E100{#:#,1,2>#}100#{100}#100
...
(76) blasphemorgulus-carta-hundrelasphemorgue = E100{#:#,1,2>#}100{#,#,1,2}100
...
(77) hundrelasphemorgue-by-deuteron = E100{#:#,1,2>#}100{#:#,1,2>#}100
(78) hundrelasphemorgue-by-triton
= E100{#:#,1,2>#}100{#:#,1,2>#}100{#:#,1,2>#}100
(79) hundrelasphemorgue-by-teterton= E100{#:#,1,2>#}*#5
...
(80) hundrelasphemorgue-by-hyperion = E100{#:#,1,2>#}*#100
...
(81) deutero-hundrelasphemorgue = E100{#:#,1,2>#}*{#:#,1,2>#}100
...
(82) terrible hundrelasphemorgue = E100{#:#,1,2>#}^^#100
(83) horrible hundrelasphemorgue = E100{#:#,1,2>#}^^^#100
(84) horrendous hundrelasphemorgue = E100{#:#,1,2>#}^^^^#100
...
E100({#:#,1,2>#}){#}({#:#,1,2>#})100
E100({#:#,1,2>#}){{#:#,1,2>#}}({#:#,1,2>#})100
E100({#:#,1,2>#}){({#:#,1,2>#}){{#:#,1,2>#}}({#:#,1,2>#})}({#:#,1,2>#})100
...
E100{{#:#,1,2>#},100,1,2}100
E100{{{#:#,1,2>#},#,1,2},100,1,2}100
...
E100{{#:#,1,2>#}:#,1,2>#}100 = E100{#:#,1,2>(#+#)}100
E100{{{#:#,1,2>#}:#,1,2>#}:#,1,2>#}100
= E100{#:#,1,2>(#+#+#)}100
...
At this point we reach the ordinal &(1). This is equivalent to {#:#,1,2>##}. This is the point at which we reach a ludicriss. The name is a combination of ludicrous with criss-cross. The "criss-cross" is in reference to the "##" applications of :#,1,2.
(85) ludicriss = E100{#:#,1,2>##}100
(86) grand ludicriss = E100{#:#,1,2>##}100#2
(87) grangol-carta-ludicriss = E100{#:#,1,2>##}100#100
...
E100{#:#,1,2>(##+#)}100
E100{#:#,1,2>(##+#+#)}100
E100{#:#,1,2>(##+#+#+#)}100
...
&(2) --> {#:#,1,2>(##+##)}
&(3) --> {#:#,1,2>(##+##+##)}
&(4) --> {#:#,1,2>(##+##+##+##)}
...
&(#) --> {#:#,1,2>###}
Here we will start coining new numbers...
(88) ludicube = E100{#:#,1,2>###}100
(89) grand ludicube = E100{#:#,1,2>###}100#2
(90) grangol-carta-ludicube = E100{#:#,1,2>###}100#100
...
&(##) --> {#:#,1,2>####}
(91) luditess = E100{#:#,1,2>####}100
(92) grand luditess = E100{#:#,1,2>####}100
...
&(###) --> {#:#,1,2>#####}
(93) ludipent = E100{#:#,1,2>#####}100 = E100{#:#,1,2>#^#}5
(94) grand ludipent = E100{#:#,1,2>#####}100#2
...
&(#^n) --> {#:#,1,2>#^(n+2)}
(95) ludihex = E100{#:#,1,2>#^#}6
(96) ludihept = E100{#:#,1,2>#^#}7
(97) ludi-ogd = E100{#:#,1,2>#^#}8
(98) ludi-ent = E100{#:#,1,2>#^#}9
(99) ludi-deck = E100{#:#,1,2>#^#}10
...
(100) luditope = E100{#:#,1,2>#^#}100
(101) grand luditope = E100{#:#,1,2>#^#}100#2
= E100{#:#,1,2>#^(luditope)}100
...
&(#^#) --> {#:#,1,2>#^#}
&(#^#^#) --> {#:#,1,2>#^#^#}
&(#^#^#^#) --> {#:#,1,2>#^#^#^#}
...
&(#^^#) --> {#:#,1,2>#^^#}
&(#^^^#) --> {#:#,1,2>#^^^#}
&(#^^^^#) --> {#:#,1,2>#^^^^#}
...
&({#,#,#}) --> {#:#,1,2>{#:#,#}} --> {#,#+2,1,2}
(102) blasphemorbid = E100{#,#+2,1,2}100 = E100{#:#,1,2>{#:#,#}}100
(103) blasphemortrid = E100{#:#+3,1,2}100 = E100{#:#,1,2>{#:3,1,2}}100
(104) blasphemortetrid = E100{#:#+4,1,2}100 = E100{#:#,1,2>{#:4,1,2}}100
(105) blasphemorputrid = E100{#:#+5,1,2}100 = E100{#:#,1,2>{#:5,1,2}}100
(106) blasphemorhexid = E100{#:#+6,1,2}100 = E100{#:#,1,2>{#:6,12}}100
(107) blasphemorheptid = E100{#:#+7,1,2}100 = E100{#:#,1,2>{#:7,1,2}}100
(108) blasphemorogdid = E100{#:#+8,1,2}100 = E100{#:#,1,2>{#:8,1,2}}100
(109) blasphemorennid = E100{#:#+9,1,2}100 = E100{#:#,1,2>{#:9,1,2}}100
(110) blasphemordecrepid = E100{#:#+10,1,2}100
...
(111) dustaculated-blasphemorgulus
= E100{#:#,1,2>{#:#,1,2}}100 = E100{#:##,1,2}2
(also blasphemorgudubbus)
(112) tristaculated-blasphemorgulus = E100{#:##,1,2}3
(also blasphemorgutrebbus)
(113) tetrastaculated-blasphemorgulus = E100{#:##,1,2}4
(also blasphemorguquabbus)
(114) pentastaculated-blasphemorgulus = E100{#:##,1,2}5
(115) hexastaculated-blasphemorgulus = E100{#:##,1,2}6
(116) heptastaculated-blasphemorgulus = E100{#:##,1,2}7
(117) ogdastaculated-blasphemorgulus = E100{#:##,1,2}8
(118) ennastaculated-blasphemorgulus = E100{#:##,1,2}9
(119) dekastaculated-blasphemorgulus = E100{#:##,1,2}10
...
{#,#+#,1,2} --> &({#,#,1,2})
{#,#+#+#,1,2} --> &(&({#,#,1,2}))
{#,#+#+#+#,1,2} --> &(&(&({#,#,1,2})))
...
{#,##,1,2} --> #*^#
(120) agoraphobia = E100{#,##,1,2}100
(121) grand agoraphobia = E100{#:##,1,2}100#2
...
(122) dustaculated-agoraphobia = E100{#:###,1,2}2
(123) tristaculated-agoraphobia = E100{#:###,1,2}3
(124) tetrastaculated-agoraphobia = E100{#:###,1,2}4
(125) pentastaculated-agoraphobia = E100{#:###,1,2}5
(126) hexastaculated-agoraphobia = E100{#:###,1,2}6
(127) heptastaculated-agoraphobia = E100{#:###,1,2}7
(128) ogdastaculated-agoraphobia = E100{#:###,1,2}8
(129) ennastaculated-agoraphobia = E100{#:###,1,2}9
(130) dekastaculated-agoraphobia = E100{#:###,1,2}10
...
#*^## --> {#:##,1,2>2}
#*^### --> {#:##,1,2>3}
...
#*^#^# --> {#:##,1,2>#}
#*^#^#^# --> {#:##,1,2>#^#}
...
#*^#^^# --> {#:##,1,2>#^^#}
#*^#^^^# --> {#:##,1,2>#^^^#}
...
#*^#*^# --> {#:##,1,2>{#:##,1,2}}
#*^#*^#*^# --> {#:##,1,2>{#:##,1,2>{#:##,1,2}}}
...
#*^^# --> {#:###,1,2}
(131) acrophobia = E100{#:###,1,2}100
(132) grand acrophobia = E100{#:###,1,2}100#2
...
(133) megalophobia = E100{#:####,1,2}100
(134) grand megalophobia = E100{#:####,1,2}100
...
(135) arithmophobia = E100{#:#####,1,2}100
(136) grand arithmophobia = E100{#:#####,1,2}100#2
...
(137) ailurophobia = E100{#:#^#,1,2}6
(138) trypophobia = E100{#:#^#,1,2}7
(139) pediophobia = E100{#:#^#,1,2}8
(140) xenophobia = E100{#:#^#,1,2}9
(141) thanatophobia = E100{#:#^#,1,2}10
...
(142) ecstasulus = E100{#:#^#,1,2}100
(143) grand ecstasulus = E100{#:#^#,1,2}100#2
...
E100{#,#^^#,1,2}100
E100{#,#^^^#,1,2}100
E100{#,#^^^^#,1,2}100
...
E100{#,#{#}#,1,2}100
E100{#,#{#{#}#}#,1,2}100
...
E100{#,{#,#,1,2},1,2}100 = E100{#,3,2,2}100
E100{#,{#,{#,#,1,2},1,2},1,2}100 = E100{#,4,2,2}100
...
E100{#,#,2,2}100
E100{#,#,3,2}100
E100{#,#,4,2}100
...
deusus-godsgodgogle = E100{#,#,#,2}100 = E100{#,#,100,2}100
treusus-godsgodgogle = E100{#,#,#,3}100 = E100{#,#,100,3}100
quadeusus-godsgodgogle = E100{#,#,#,4}100 = E100{#,#,100,4}100
alternatively...
sacriligulus = E100{#,#,1,3}100
hereticulus = E100{#,#,1,4}100
apostatulus = E100{#,#,1,5}100
...
thohtothihlith = E100{#,#,1,#}100
(Also thoh for short)
General Gogulus = E100{#,#,#,#}100
(also tetrentriculus )
At this point we seem to hit another impasse ... if only we had a notation to extend an ordinal function ... oh wait, we already invented such a notation ... it's called xE^. To allow the rules of xE^ to extend our new ordinal function &(a), we need to relate it back to up-arrows. Let...
a*^#[n] = &(&(&( ... &(&(&(a+1))) ... ))) w/n &'s
The ' *^ ' is a new operator. Note the ' a+1 ' nested within the &'s. This is to avoid the fixed point problem which occurs with unary-ordinal functions. Already this gives us a lot of power. Consider the following ...
#*^#[n] = &(&(&( ... &(&(&(#+1))) ... ))) w/n &'s
This is already sufficient to keep up with an agoraphobia sequence. Simply use...
E100#*^#100 ~ agoraphobia
E100#*^#100#2 ~ grand agoraphobia
E100#*^#100#3 ~ grand grand agoraphobia
etc.
The new operator can be combined with all the pre-existing operators, so we can get things like ...
(#*^#)^#
(#*^#)^##
...
(#*^#)^^#
(#*^#)^^#>#
...
(#*^#)^^##
...
(#*^#)^^^#
...
(#*^#){#}#
{#*^#,#,1,2}
...
{#*^#,#+1,1,2}
{{#*^#,#+1,1,2},#+1,1,2}
{{{#*^#,#+1,1,2},#+1,1,2},#+1,1,2}
...
In this way we reach &(#*^#+1). The +1 is necessary to keep this from collapsing to a mere &(#*^#)[n] = #*^#[n+1]. Because of our definition of (a)*^#, we can now create multiple fixed points for the &-function. So we can have...
(#*^#)*^#[n] = &(&(&( ... &(&(&(#*^#+1))) ... ))) w/n &'s
Furthermore let...
#*^## = (#*^#)*^#
... o_0;
see where I'm going with this? Now we can create a second level of ordinal hyper-operators stacked on top of the original! We have already set things up so that we have a binary ordinal operator (a)*^(b) which is well defined as long as b is not a hyper-sum. So we can have...
#*^### = (#*^##)*^#
#*^#### = (#*^###)*^#
...
#*^#^#
...
#*^#^^#
#*^#^^^#
...
#*^#{#}#
#*^{#,#,1,2}
#*^&(1)
...
#*^#*^#
#*^#*^#*^#
#*^#*^#*^#*^#
...
Above all this we can use #*^^#. Now let...
#*^^#[n] = #*^#*^#*^#*^ ... *^#*^#*^# w/n #s
We can coin...
astralthrathoth = E100#*^^#100
grand astralthrathoth = E100#*^^#100#2
grand grand astralthrathoth = E100#*^^#100#3
What's incredible is things are now set up that we can actually keep going without having to invent any new rules. Just watch ...
(#*^^#)*^#[n] = &(&(&( ... &(&(&(#*^^#+1))) ... ))) w/n &'s
...
(#*^^#)*^(#*^^#)
...
(#*^^#)*^^#
((#*^^#)*^^#)*^^#
...
#*^^#>#
#*^^#>#*^^#
#*^^#>#*^^#>#*^^#
...
#*^^##
#*^^###
...
#*^^#^#
#*^^#^^#
#*^^#^^#^^#
...
#*^^#^^^#
#*^^#{#}#
#*^^{#,#,1,2}
#*^^{#,#+1,1,2}
#*^^&(1)
...
#*^^#*^#
#*^^#*^#*^#
...
#*^^#*^^#
#*^^#*^^#*^^#
...
#*^^^#
#*^^^^#
...
etc.
The upshot is the ability to extend the &-function very far without having to invent a bunch of new tricks ... we just recycle the old rules. As you can see we now have a set of ordinary hyper-operators and a new set of super-hyper-operators! And it gets more insane ...
#*{#}#[n] = #*^^^ ... ^^^# w/n ^s
#*{##}#
#*{#^#}#
#*{#^^#}#
#*{#^^^#}#
...
#*{#{#}#}#
#*{#{#{#}#}#}#
...
#*{{#,#,1,2}}#
...
#*{&(1)}#
#*{#*^#}#
...
#*{#*{#}#}#
#*{#*{#*{ ... #*{#*{#*{#}#}#}#... }#}#}#
...
*{#,#,1,2}
*{#,#+1,1,2}
*&(1)
*&(#)
*&(*&(#))
*&(*&(*&(#)))
*&(*&(*&(*&(#))))
...
Now we just create...
(a)**^#[n] = *&(*&(*&( ... *&(*&(*&(a+1))) ... ))) w/n *&'s
o_0;;
That's right ... we are going to create multiple stacks of special hyper-operators. We can now have things like...
#**^#
#**^^#
#**^^^#
...
**{#,#,1,2}
**&(#)
**&(**&(#))
...
#***^#
#***^^#
#***^^^#
...
***{#,#,1,2}
***&(#)
***&(***&(#))
...
#****^#
#*****^#
#******^#
etc.
We use this notation to create the next whopper ... the gorgonghoulgog ...
gorgonghoulgog = E100***** ... *****{#,#,1,2}100 w/100 *'s
Gorgonghoulgog is used to define ...
grand gorgonghoulgog = E100***** ... *****{#,#,1,2}100 w/gorgongallgog *'s
The grand gorgonghoulgog is used to define the gathering. The gathering is a vast assembly of truly vast eldritch abominations, assembled to speak of incomprehensible things amongst themselves ( as Douglas Reay suggested they might). Imagine that each positive integer from a blasphemorgulus to a grand gorgonghoulgog were assembled in one place. The gathering is defined as the sum of all positive integers from a blasphemorgulus to grand gorgonghoulgog. In other words ...
the gathering
=
[(grand gorgonghoulgog)2-(blasphemorgulus)2+(grand gorgonghoulgog)+(blasphemorgulus)]/2
The Gathering has been hosted by the grand gorgonghoulgog himself, a gorgonghoulgog-star general. He is the first guest to arrive. He is followed by and grand gorgonghoulgog minus one, then the grand gorgonghoulgog minus two. This continues for an inconceivably long time until the last guest arrives ... the blasphemorgulus ... the smallest of the guests!
There are some interesting observations to be made about the gathering. Firstly the number in attendance is virtually the same as size of the largest member in attendance (the grand gorgonghoulgog). Assuming the gathering is arranged in a grid pattern with the largest members in the center and smaller members distributed in a spiral pattern around the center, it turns out that all the numbers from a blasphemorgulus to E100***...***{#,#,1,2}100 w/(gorgonghoulgog-1) *'s would all be situated at an infinitesimal point on one of the sides of the grid! In other words the small members are vastly outnumbered by the large members to the point where they are forced to created their own isolated gathering at the outskirts of the larger gathering, or risk being lost amongst super-giants. Rather than form a simple line, which would isolate members of roughly the same size from each other it is better for them to gather and form their own grid containing their own peers. This 2nd gathering will in turn be too large for a yet smaller subset from blasphemorgulus to E100***...**{#,#,1,2}100 w/(gorgonghoulgog-2) *'s, thus forming a 3rd gathering, and so on, and so on for a gorgonghoulgog gatherings ....
The gathering as a whole dwarfs the grand gorgonghoulgog by a factor of himself, yet in the grander scheme of things the gathering is still in the googological neighborhood of a grand gorgonghoulgog (In otherwords the gathering and the grand gorgonghoulgog are googologically the same size).
In any case we can continue...
Let *(#)(a)[n] = ***...***(a) w/n *'s
and we get...
gorgonghoulgog = E100*(#){#,#,1,2}100 = E100*(100){#,#,1,2}100
grand gorgonghoulgog = E100*(#){#,#,1,2}100#2
= E100*(#){#,#,1,2}(E100*(#){#,#,1,2}100)
= E100*(#){#,#,1,2}(gorgonghoulgog) =
E100*(gorgonghoulgog){#,#,1,2}100
... and ...
the gathering =
[(E100*(#){#,#,1,2}100#2)^2-(E100{#,#,1,2}100)^2+E100*(#){#,#,1,2}100#2+E100{#,#,1,2}100]/2
Insane ... yet we can now go further still. Let the argument of *(a) be any ordinal we can already construct, and nest this new function ...
We can begin by simplifying matters and letting...
*(a) = *(a){#,#,1,2}
or some other suitable default value for the argument. Then we can say ...
*(#) = *(#){#,#,1,2}
*(*(#)) = *(*(#){#,#,1,2}){#,#,1,2}
*(*(*(#))) = *(*(*(#){#,#,1,2}){#,#,1,2}){#,#,1,2}
...
And now we reach the pinnacle of this mad ascent ...
transmorgrifihgh
= E100*(*(*(*(*( ... *(*(*(*(*(#))))) ... )))))100
w/100 *'s
grand transmorgrifihgh
= E100*(*(*(*(*( ... ... *(*(*(*(*(#))))) ... ... )))))100
w/transmorgrifihgh *'s
grand grand transmorgrifihgh
= E100*(*(*(*(*( ... ... *(*(*(*(*(#))))) ... ... )))))100
w/grand transmorgrifihgh *'s
We can also have ...
grand grand transmorgrifihgh with croutons
=
E(grand transmorgrifihgh)*(*(*( ... ... *(*(*(#))) ... ... )))(grand transmorgrifihgh)
w/grand transmorgrifihgh *'s
Just kidding! The above is just a salad number being used to illustrate a point. Increasing the arguments at this stage does little to improve the size of a grand grand transmorgrifihgh! To prove this let...
/ = *(*(*( ... ... *(*(*(#))) ... ... ))) w/transmorgrifihgh *'s
% = *(*(*( ... ... *(*(*(#))) ... ... ))) w/grand transmorgrifihgh *'s
By this we have...
grand transmorgrifihgh = E100/100
grand grand transmorgrifihgh = E100%100
grand grand transmorgrifihgh with croutons = E(E100/100)%(E100/100)
Now just consider a mere E100%100#2 ...
E100%100#2 = E100%(E100%100) = E100%(grand grand transmorgrifihgh)
This is already larger than grand grand transmorgrifihgh with croutons since the 2nd argument is so much larger. This completely overwhelms the benefit of having E100/100 in the first argument. Yet E100%100#2 is vanishingly small compare to ...
grand grand grand transmorgrifihgh = E100*(*(*( ... *(*(*(#))) ... )))100
w/grand grand transmorgrifihgh *'s
which is vanishingly small compare to ...
grand grand grand grand transmorgrifihgh = E100*(*(*( ... *(*(*(#))) ... )))100
w/grand grand grand transmorgrifihgh *'s
The above may already suggest to you some ways to continue ... we might for example create a series of such ordinal-functions, each indexed with a new symbol, which continue to nest into themselves to form the next level of the notation. However at this point things are quite ad hoc. Although we could continue it would be better to address the root of the problem before creating further generalizations. In the long run we will avoid difficulties down the road and we will also get to streamline the notation. The root of the problem is that we have at this point completely abandoned the approach of extending arrays ... an approach which promises to quickly make the above obsolete. The satisfactory continuation of Hyperion-arrays however will require a better understanding of array-structures at this level. That is an area of future research and development.
In the meantime however we will go one level more INsAnE! This will take us well beyond anything we've yet considered and yet ... it still will not even come close to legion-space. This new extension which extends on Hyper-Hyper-Extended-Cascading-E Notation (##xE^ which includes the arrays-of-hyperions, & and * ordinal-functions), already an extension on Hyper-Extended-Cascading-E Notation (#xE^ which covered everything below {#,#,1,2} and was the largest formally defined system), is called Solidus-Extended Cascading-E Notation (/xE^), and it introduces a new symbol, the solidus, "/".
We begin with a new definition as usual...
a/^#[n] = *(*(*(...*(*(a+1))...))) w/n *'s
the use of the "slash" or "solidus" , "/" , for the next symbol was suggested by Aarex Tiaokhiao. Recently he has used a polyadic extension of the *-operator.
Of coarse... we already have all the structure necessary to extend (*this) quites a ways...
transmorgrifihgh ~ E100#/^#100
grand transmorgrifihgh ~ E100#/^#100#2
grand grand transmorgrifihgh ~ E100#/^#100#3
grand grand grand transmorgrifihgh ~ E100#/^#100#4
grand grand grand grand transmorgrifihgh ~ E100#/^#100#5
...
hundred-ex-grand transmorgrifihgh ~ E100#/^#100#101
This is vashingly tiny compare to...
transmorgrifact = E100(#/^#)^#100
which is vanishingly tiny compare to ...
terrible transmorgrifihgh = E100(#/^#)^^#100
horrible transmorgrifihgh = E100(#/^#)^^^#100
horrendous transmorgrifihgh = E100(#/^#)^^^^#100
heptorrendous transmorgrifihgh = E100(#/^#){5}#100
ogdorrendous transmorgrifihgh = E100(#/^#){6}#100
ennorrendous transmorgrifihgh = E100(#/^#){7}#100
There is a limit to how far we can extend on the name "transmorgrifihgh" using already established constructs ... but this doesn't stop the notation from just going on and on and on ...
E100(#/^#){8}#100
E100(#/^#){9}#100
E100(#/^#){10}#100
E100(#/^#){100}#100
E100{#/^#,#,#}100
E100{#/^#,#,1,2}100
E100{#/^#,#+1,1,2}100
...
E100&(#/^#+1)100
E100&(&(#/^#+1))100
E100&(&(&(#/^#+1)))100
...
E100(#/^#)*^#100
o_0;;
astronomcally-terrible transmorgrifihgh = E100(#/^#)*^^#100
astronomically-horrible transmorgrifihgh = E100(#/^#)*^^^#100
(heh heh ... astromical is such an understatement here!)
E100(#/^#)*^^^^#100
E100(#/^#)*{100}#100
...
E100*{#/^#,#,#}100
E100*{#/^#,#,1,2}100
E100*{#/^#,#+1,1,2}100
...
E100*&(#/^#+1)100
E100*&(*&(#/^#+1))100
E100*&(*&(*&(#/^#+1)))100
...
E100(#/^#)**^#100
double-astronomically-terrible transmorgrifihgh
= E100(#/^#)**^^#100
E100(#/^#)**^^^#100
E100(#/^#)**^^^^#100
...
E100(#/^#)***^#100
triple-astronomically-terrible transmorgrifihgh
= E100(#/^#)***^^#100
...
E100(#/^#)****^#100
quadruple-astronomically-terrible transmorgrifihgh
= E100(#/^#)****^^#100
... ... ...
E100(#/^#)**********^#100
E100(#/^#)*(100)^#100
E100*(100){#/^#,#,1,2}100
E100*(*(#)){#/^#,#,1,2}100
E100*(*(*(#))){#/^#,#,1,2}100
E100*(*(*(*(#)))){#/^#,#,1,2}100
...
E100*(*(*(*( ... *(*(*(*(#)))) ... )))){#/^#,#,1,2}100
... oh thank goodness looks like were finally getting somewh--
E100*(#/^#){#/^#,#,1,2}100
-- oh hell no o_0;;;
E100*((#/^#)^#){#/^#,#,1,2}100
... 1 , 2 , skip a few ... 99 ...
E100*(*(*(*(*(*(*(*(*(*(... *(*(*(*(*(*(*(*(*(*(#/^#){#/^#,#,1,2}){#/^#,#,1,2}){#/^#,#,1,2}){#/^#,#,1,2}){#/^#,#,1,2}){#/^#,#,1,2}){#/^#,#,1,2}){#/^#,#,1,2}){#/^#,#,1,2}){#/^#,#,1,2} ...){#/^#,#,1,2}){#/^#,#,1,2}){#/^#,#,1,2}){#/^#,#,1,2}){#/^#,#,1,2}){#/^#,#,1,2}){#/^#,#,1,2}){#/^#,#,1,2}){#/^#,#,1,2}){#/^#,#,1,2}100
At this point a redefinition of the *function is in order...
*(a) = *(a){a,#,1,2}
This ends up becoming a nesting nightmare ...
*(#/^#) = *(#/^#){#/^#,#,1,2}
*(*(#/^#)) = *(*(#/^#){#/^#,#,1,2})
= *(*(#/^#){#/^#,#,1,2}){*(#/^#){#/^#,#,1,2},#,1,2}
*(*(*(#/^#)))
= *(*(*(#/^#){#/^#,#,1,2}){*(#/^#){#/^#,#,1,2},#,1,2}){*(*(#/^#){#/^#,#,1,2}){*(#/^#){#/^#,#,1,2},#,1,2},#,1,2}
etc.
However this redefinition allows us to continue much further. Next we have //--
E100(#/^#)/^#100
-- make it STOP!!! ...
E100((#/^#)/^#)/^#)100
E100(((#/^#)/^#)/^#)/^#100
...
E100#/^#^#100
...
E100#/^#/^#100
E100#/^#/^#/^#100
...
slaschelon-tethrathoth = E100#/^^#100
E100#/^^^#100
E100#/^^^^#100
...
E100#/{100}#100
E100/{#,#,#}100
...
E100/{#,#,1,2}100
E100/{#,#+1,1,2}100
...
E100/&(1)100
... you've got to be kidding -_- ...
E100/&(#)100
E100/&(/&(#))100
E100/&(/&(/&(.../&(/&(#)) ...)))100
... and thus we reach the amazing //--
E100#/*^#100
F--K!!! ...
E100#/**^#100
E100#/***^#100
E100#/****^#100
...
E100/*(100){#,#,1,2}100
E100/*(/*(100){#,#,1,2}){#,#,1,2}100
...
slaschelon-transmorgrifihgh
= E100/*(/*(/*(/*( ... /*(/*(/*(#))) ... ))))100 w/100 /*s
which is of coarse just a member of some fundamental sequence of some larger ordinal...
E100#//^#100
and of coarse this is just the beginning of the next insane level. We can now extend the // using up-arrows, a modified //& function and then //* //** //***, nesting this leads to ///...
E100#///^#100
nesting ///*(a) leads to...
E100#////^#100
nesting ////*(a) leads to...
E100#/(5)^#100
... and now even the number of / is an ordinal and we can nest /(a)...
hectalaceron = E100#/(100)^#100
...
grand hectalaceron = E100#/(#)^#100#2
...
super-hectalaceron = E100#/(#/(100)^#)^#100
super-super-hectalaceron = E100#/(#/(#/(100)^#)^#)^#100
...
at this point we need a nifty short hand for /(a). Based on the star operator we just use...
/(a) = /(a){a,#,1,2}
This allows for the introduction of...
iniquifihgh (/in-eh-qu-i-f-I-g/)
= E100/(/(/(/( ... /(/(/(/(#)))) ... ))))100 w/100 "/"s
grand iniquifihgh =E100/(/(/(/( ... /(/(/(/(#)))) ... ))))100 w/iniquifihgh "/"s
To go further still with this now completely ad hoc system we need a new symbol after the * and /. Here a generalization is desired. I'll use...
/x
/xx
/xxx
/xxxx
etc.
for the continuation...
Let...
a/x^#[n] = /(/(/(/(.../(/(/(a+1)))...)))) w/n "/"s
a/xx^#[n] = /x(/x(/x(/x(.../x(/x(/x(a+1)))...)))) w/n "/x"s
a/xxx^#[n] = /xx(/xx(/xx(/xx(.../xx(/xx(/xx(a+1)))...)))) w/n "/x"s
a/xxxx^#[n] = /xxx(/xxx(/xxx(/xxx(.../xxx(/xxx(/xxx(a+1)))...)))) w/n "/x"s
Now all hell breaks loose! Now we can have any combination of these symbols, forming a multi-argument lattice of ordinal recursion (which leads to even more insane levels of primitive recursions and diagonalization)...
iniquifihgh ~ E100#/x^#100
grand iniquifihgh ~ E100#/x^#100#2
...
E100#/x^^#100
E100#/x^^^#100
E100#/x^^^#100
...
E100#/x*^#100
E100#/x*^^#100
...
E100#/x**^#100
... ... ...
E100#/x****^^^^100
...
E100#/x/^#100
E100/x/(#)100
E100/x/(/x/(#))100
E100/x/(/x/(/x/(#)))100
...
E100#/x/*^#100
...
E100#/x/////////**********^^^^^^^^^^100
...
E100#/x/x^#100
...
E100#/x/x////****^^^^#100
...
E100#/x/x/x^#100
...
E100#/x/x/x/x////****^^^^#100
oxoxyoxl
(/aw-ks-aw-ks-E-aw-ks-l/)
= E100#/x/x/x/x ... /x/x/x/x^#100 w/100 "/x"s
grand oxoxyoxl
= E100#/x/x/x/x/x ... ... ... /x/x/x/x/x^#100 w/oxoxyoxl "/x"s
E100/x(100){#,#,1,2}100
E100/x(/x(#))100
E100/x(/x(/x(#)))100
...
conflagrifihgh
= E100/x(/x(/x(/x(...(/x(/x(/x(#)))...))))100 w/100 "/x"s
grand conflagrifihgh
= E100/x(/x(/x(/x(...(/x(/x(/x(#)))...))))100 w/conflagrifihgh "/x"s
...
conflagrifihgh ~ E100#/xx^#100
grand conflagrifihgh ~ E100#/xx^#100#2
...
E100#/xx/x/*^#100
E100/xx/x/*&(1)100
...
E100#/xx/x/**^#100
...
E100#/xx/xx^#100
E100#/xx/xx/xx^#100
...
E100/xx(#)100
E100/xx(/xx(#))100
E100/xx(/xx(/xx(#)))100
...
E100#/xxx^#100
...
E100#/xxxx^#100
...
E100#/xxxxx^#100
...
E100#/xxxxxx^#100
E100#/xxxxxxx^#100
E100#/xxxxxxxx^#100
meowmix
= E100#/xxxxxxxx/xxxxxxx/xxxxxx/xxxxx/xxxx/xxx/xx/x^#100
meowmix with croutons
= E100#/xxxxxxxx/xxxxxxx/xxxxxx/xxxxx/xxxx/xxx/xx/x********^#100
meowmix with croutons-and-a-fork
= E100#/xxxxxxxx/xxxxxxx/xxxxxx/xxxxx/xxxx/xxx/xx/x********^^^^#100
hundreadrifihgh
= E100#/xxxxxxxxxx...xxxxxxxxxx^#100 w/100 x's
grand hundreadrifihgh
= E100#/xxxxx ... ... ... xxxxx^#100 w/hundreadrifihgh x's
hundreadrifihgh already reaches the level of Aarex's transmorgrifihghundred.
Getting pretty loopy ... but we can keep going by nesting x's! This quickly takes us beyond what we can get using Veblen's methodology...
Here we have...
(x^n) = xxxx...xxxx w/n x's
Now we simplify matters slightly by reverse engineering our new super-powered x-function...
/x^0 --> /
/x^1 --> /x
/x^2 --> /xx
/x^3 --> /xxx
/x^4 --> /xxxx
etc.
Also let...
x^a = x^a(a) = /x^a(a)
Now madness ensues ... HA HA HA!!!
hundreadrifihgh = E100#(x^#)^#100
grand hundreadrifihgh = E100#(x^#)^#100#2
...
E100x^#100 = E100/x^#(#)100 = E100/x^#(#){#,#,1,2}100
= E100/x^100(#){#,#,1,2}100
x^#+# exhibits the same growth rate as the hundreadrifihgh-sequence. But better yet, when the argument of x^a is a successor ordinal, we can treat it as a new symbol after all the previous symbols. Specifically each separator is able to extend itself using itself and all lower separators, including limit cases. For example...
E100x^#/x^#100 = E100x^#/xxx ... 100xs ... xxx(100){#,#,1,2}100
Note that all of "xxx ... 100xs ... xxx(100){#,#,1,2}" is acting to extend x^#! Next we have...
E100x^(#+1)100 = E100x^#(x^#(x^#(...(x^#(#))...)))100
with each increase in the argument of x^a , we are iterating the set of previous x^a. So now ordinals are serving to enumerate iterations of ordinal recursions ... x_x getting dizzy yet?!
E100x^(#+2)100 = E100x^(#+1)(x^(#+1)( ... (x^(#+1)(#))...))100
... of coarse now it can be made inconceivably worse than anything we've seen so far because we can now use any of the ordinals we've yet constructed, up to and including ones which use our new x-function!
E100x^(#+#)100 = E100x^(#+100)100
...
E100x^(##)100
...
E100x^(#^#)100
...
E100x^(#^^#)100
E100x^({#,#,1,2})100
E100x^(&(1))100
...
E100x^(#*^#)100
...
E100x^(#/^#)100
E100x^(#/x^#)100
E100x^(#/xx^#)100
E100x^(#/xxx^#)100
E100x^(#/xxxx^#)100
...
E100x^x^#100
E100x^x^x^#100
E100x^x^x^x^#100
E100x^x^x^x^x^#100
...
E100x^^#100
E100(x^^#)^#100
E100(x^^#)^^#100
E100(x^^#)*^#100
E100(x^^#)**^#100
...
E100(x^^#)/^#100
E100(x^^#)/x^#100
E100(x^^#)/xx^#100
E100(x^^#)/xxx^#100
E100(x^^#)/xxxx^#100
...
E100(x^^#)/(x^#)^#100
E100(x^^#)/(x^x^#)^#100
...
E100/(x^^#)/(x^^#)100
E100/(x^^#)/(x^^#)/(x^^#)100
E100/(x^^#)/(x^^#)/(x^^#)/(x^^#)100
...
E100/(x^^#)(100)100
E100/(x^^#)(/(x^^#)(/(x^^#)(...(/(x^^#)(#)...))100
... E100/(x^^#*x)100
E100/(x^^#*x^2)100
...
E100/(x^^#*x^^#)100
E100/({x^^#}^#)100
E100/({x^^#}^{x^^#})100
E100/(x^^#>2)100
E100/(x^^#>2*x)100
E100/(x^^#>3)100
...
E100/(x^^#>x^^#)100
...
E100/(x^^##)100
...
E100/(x^^###)100
...
E100/(x^^#^#)100
...
E100/(x^^x^^#)100
...
E100/(x^^^#)100
E100/(x^^^^#)100
...
E100/(x{100}#)100
...
E100/({x,#,#})100
E100/({x,#,1,2})100
...
E100/(&(x+1))100
...
E100/(x*^#)100
E100/(x**^#)100
E100/(x***^#)100
E100/(x****^#)100
...
... hehe...he...maakit STOP!... aaaaaaghhhh!!! x_x
E100/(x*(#)^#)100
E100/(x/^#)100
E100/(x/x^#)100
E100/(x/xx^#)100
E100/(x/xxx^#)100
E100/(x/xxxx^#)100
...
E100/(x/(x^100)^#)100
...
E100/(x/(x^#))100
E100/(x/(x^x^#))100
E100/(x/(x^x^x^#))100
E100/(x/(x^x^x^x^#))100
...
E100/(x/(x^^#))100
...
E100/(x/(x^^^#))100
...
E100/(x/(x/(x^#)))100
E100/(x/(x/(x/(x^#))))100
...
babbulbufihgh
(/b-ah-b-O-l-b-uh-f-I-g/)
= E100/(x/(x/(x/(...(x/(x/(x^#)))...)))100
(Aarex called this number golapuifihgh , but this number IS NOWHERE NEAR a golapulus! A golapulus is so much larger than a babbulbufihgh that such a comparison is laughable! )
... that's it right ... RiGht!?! We could keep going but the notation starts tripping over itself. We are already pushing it with some quite dicey notation and extremely informal sequences. Aarex goes for one further extension in which /2 diagonalizes over the entire system of /xE^. He then proceeds to nest /2 's in the same way we nested / 's to form /3 and so on. This can be continued until /# and then we can diagonalize over /a with // representing the first fixed-point of a-->/a. This of coarse can be taken further until we have ///.... Aarex ends with the "number" created by 100 layers of subscripting " / "s and calls this number bulbarepeatihgh. I'll suggest the alternative:
solidifihgh = E100/_(/_(/_(/_(/_ ... (/_(/_#)) ... ))))100
Despite how far we've pushed past the now humble transmorgrifihgh or even iniquifihgh, we have still gotten virtually NOWHERE in array-space!!! Getting even to a golapulus will require radically new methods. These methods are not powerful enough and are already being pushed to the breaking-point. The above approach will need to be streamlined and related back to arrays-of-hyperions. All the work is still ahead of us!
Despite the lack of a formal, or even vague informal definition, I'm going to continue after this point but let me stress that what follows after this point is not fully defined yet, and are merely planned constructions. I also can't say with any certainly how far they are along the fast growing hierarchy or BEAF. These are questions that need to be worked out in future articles. Without further ado let's finish up the blasphemorgulus group ...
E100{#,#+2,1,2}100
E100{#,#+3,1,2}100
E100{#,#+4,1,2}100
...
blasphemorgudubbus = E100{#,#+#,1,2}100
blasphemorgutrebbus = E100{#,#+#+#,1,2}100
blasphemorguquabbus = E100{#,#+#+#+#,1,2}100
...
E100{#,##,1,2}100
E100{#,###,1,2}100
E100{#,####,1,2}100
...
E100{#,#^#,1,2}100
E100{#,#^^#,1,2}100
E100{#,#^^^#,1,2}100
E100{#,#^^^^#,1,2}100
...
E100{#,#{#}#,1,2}100
E100{#,#{#{#}#}#,1,2}100
...
E100{#,{#,#,1,2},1,2}100 = E100{#,3,2,2}100
E100{#,{#,{#,#,1,2},1,2},1,2}100 = E100{#,4,2,2}100
...
E100{#,#,2,2}100
E100{#,#,3,2}100
E100{#,#,4,2}100
...
deusus-godsgodgogle = E100{#,#,#,2}100 = E100{#,#,100,2}100
treusus-godsgodgogle = E100{#,#,#,3}100 = E100{#,#,100,3}100
quadeusus-godsgodgogle = E100{#,#,#,4}100 = E100{#,#,100,4}100
...
General Gogulus = E100{#,#,#,#}100
...
ogdodgulus = E100{#,#,#,#,#,#,#,#}100
demagogue = E100{#,10(1)2}100 = E100{#,#,#,#,#,#,#,#,#,#}100
...
ominongulus = E100{#,100(1)2}100
= E100{#,#,#,#,#,#,#,#,#,#, ... ,#,#,#,#,#,#,#,#,#,#}100
w/100 #s
pseudomonarchia daemonum = E100{#,#(1)2}44,435,622
= E100{#,#,#,#,#,#,#,#,#,#, ... ,#,#,#,#,#,#,#,#,#,#}100
w/44,435,622 #s
grand ominongulus = E100{#,#(1)2}100#2 = E100{#,#(1)2}ominongulus
grand pseudomonarchia daemonum = E100{#,#(1)2}44,435,622#2
= E100{#,#(1)2}(pseudomonarchia daemonum)
...
hecatonchirechelon = E100{#,#(1)#}100 = E100{#,#(1)100}100
(/h-eh-k-ah-t-ah-n-ch-I-r-eh-sh-eh-l-ah-n/)
goxxogogulus = E100{100x100&#}100
cloxxogogulus = E100{100x100x100&#}100
teroxxogogulus = E100{100^4&#}100
...
brobdingnagongule = E100{100^100&#}100
lugubrigoth = E100{#^^#&#}100
kekrakunge = E100{#^^^#&#}100
giygas = 616^666{{#,#,#,#,#,#}&#}666
... you can not grasp the true form of this number ... if you could you could grasp the true form of giygas's attack ...
perfect giygas = 616^666{#&#&#}666
super perfect giygas = 616^666{{#,#,#,#,#,#}&#&#}666
...
dio fa = E100{#&#&#&#&#&#&#&#&#&#}100
...
Sprach Zarathustra
=
E100{#&#&#&#&#&#&#&#&#&#& ... &#&#&#&#&#&#&#&#&#&#}100
w/100 #s
grand Sprach Zarathustra
=
E100{#&#&#&#&#&#&#&#&#&#& ... &#&#&#&#&#&#&#&#&#&#}100
w/Sprach Zarathustra #s
grand grand Sprach Zarathustra
=
E100{#&#&#&#&#&#&#&#&#&#& ... &#&#&#&#&#&#&#&#&#&#}100
w/grand Sprach Zarathustra #s
etc.
...
Thus Sprach Zarathustra
=
????(yet to be defined)????
yog-sothoth
=
????(yet to be defined)????
...the end?!?!
Transmorgrifihgh
Regiment
Members: ???
transmorgrifihgh = E100{#,#,1,1,2}100
E100{#,##,1,1,2}100
E100{#,###,1,1,2}100
E100{#,3,2,1,2}100 = E100{#,{#,#,1,1,2},1,1,2}100
E100{#,#,2,1,2}100
E100{#,#,3,1,2}100
...
E100{#,#,#,1,2}100
E100{#,#,##,1,2}100
...
E100{#,3,1,2,2}100
E100{#,#,1,2,2}100
E100{#,#,1,3,2}100
...
E100{#,#,1,#,2}100
...
E100{#,#,1,1,3}100
...
E100{#,#,1,1,#}100
pententriculus = E100{#,#,#,#,#}100
E100{#,3,1,1,1,2}100 = E100{#,#,#,#,{#,#,#,#,#}}100
Iniquifihgh
Regiment
iniquifihgh = E100{#,#,1,1,1,2}100
hexentriculus = E100{#,#,#,#,#,#}100
Conflagrifihgh
Regiment
conflagrifihgh = E100{#,#,1,1,1,1,2}100
heptentriculus = E100{#,#,#,#,#,#,#}100
E100{#,#,1,1,1,1,1,2}100
octentriculus = E100{#,#,#,#,#,#,#,#}100
E100{#,#,1,1,1,1,1,1,2}100
ennentriculus = E100{#,#,#,#,#,#,#,#,#}100
E100{#,#,1,1,1,1,1,1,1,2}100
deka-entriculus = E100{#,#,#,#,#,#,#,#,#,#}100
= E100{#,#(1)2}10
hecta-entriculus = E100{#,#(1)2}100
Ominoustrous
Regiment
ominoustrous = E100{#,#(1)2}100
...
E100{#,#+1(1)2}100
E100{#,#+2(1)2}100
...
E100{#,#+#(1)2}100
...
ominoustrothoth? = E100{#,#,2(1)2}100 --> /x^^#
E100{#,#,2,(1)2>2}100 --> /(x^^#)^^#
E100{#,##,2(1)2}100 --> /x^^##
E100{#,###,2(1)2}100 --> /x^^###
E100{#,#,1,2(1)2}100 --> /{x,#,1,2}
E100{#,#(1)3}100 --> /x^/(x^#)#
E100{#,#,2(1)3}100 --> /x^/(x^^#)#
babbulbufihgh --> E100{#,#(1)#}100
...
E100{#,#(1)3}100
E100{#,#,2(1)3}100
...
thaletothilith? = E100{#,#(1)#}100
(also babbulbufihgh )
E100{#,#(1)(1)2}100
= E100{#,#,#, ... ,#,#,#(1)#,#,#, ... ,#,#,#}100
w/200 #s
apocalypticus?
E100{#,#(2)2}100
E100{#,#(((((((((((((....(0,1)1)1)1)...)1)2}100 ~ w/100 1s
Let / diagonalize over the BHO tetrational-array-array system.
Then
shub-niggerath = E100{#,#/#}100 or higher.
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