E4 - Grangol regiment
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GRANGOL REGIMENT
Category 2
Regiment block 2
Members: 376 (188 original + 188 extension!!! YIKES!!!)
(890 - 1265)
[Tetration to pentation level]
Level 1 | Stage 2-1
Stage 2-1 ~ In the grangol regiment, we reached the tetration level of the Extensible-E series. New roots coming out.
Grangol regiment beginnings
Now for something a little more interesting. Let's begin by extending the "googol series" to insane heights. Let a googol = E100, be "step 1". Let a googolplex = EE100 be "step 2". Let a googolduplex = EEE100 be "step 3". Continue this way until you reach the 100th step.
This is the sophomore regiment of the Extensible-E system. There is some new kind of number. Here I call it "grangol", which is short for "grand googol". Now we can say:
(890) grangol ☆★✪ = E100#100 = EEEEE ... ... EEEEE100 (w/100 "E"s) =
10^10^10^10^10^ ... ... ... ... ... ... ^10^10^10^10^10^100 (w/100 Tens)
(Note: The grangol is comparable to the giggol, though it's "slightly" larger)
That's a pretty cool number. We can also have a ...
(891) grangolbit = 2^100#100 = E[2]100#100
and a ...
(892) grangolbyte = 8^100#100 = E[8]100#100
But ... you might be thinking ... these numbers aren't much larger than a hectalogue (E1#100), and are certainly smaller than even a chilialogue (E1#1000). This is true. There is some overlap here between the guppy regiment and the grangol regiment. So just to prove a point let's push the whole -logue idea to the limit. Then I'll show that we can still beat this with tricks exclusive to the grangol regiment. First to go further we loosen the requirement that the argument for (n)-logue need be in greek. Thus we can use our googolism's to bootstrap us to even larger values. Here are some examples...
But to go much further than this we can just loosen the requirement that the argument be in greek. With this in mind I will coin the largest numbers of this regiment...
Let's peak into another naming system on whether the value should be Ex#x.
To define this naming system, drop "gol" from "grangol" to make it "gran-", followed by the respective guppy regiment base googolisms, based off the Googology Wiki user ARsygo. So,
(893) granguppy = E20#20 = EEEEEEEEEEEEEEEEEEEE20 (20 "E"s) =
10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^200 (20 tens)
(894) granminnow = E25#25
(895) grangoby = E35#35
(896) grangogol = E50#50
(897) granogol = E80#80
(898) graneceton = E303#303
Here the number graneceton is E303#303, but it sounds dull, so I have to use the eceto- prefix to make ecetonates, which replaces 100 as a prime argument with 303. So we have...
(899) eceto-grangol = E303#303 = EEEEE ... ... EEEEE303 (w/303 "E"s) =
10^10^10^10^10^ ... ... ... ... ... ... ^10^10^10^10^10^100 (w/303 Tens)
But why... I am not done with the n-ary system yet. I am going to fill up other bases from guppy regiment. Say, we already have:
grangolbit = E[2]100#100
...then we will have an alternative name called...
(900) binary-grangol = E[2]100#100
...and...
grangolbyte = E[8]100#100
...then...
(901) octal-grangol = E[8]100#100
We can also have:
(902) ternary-grangol = E[3]100#100
(903) quaternary-grangol = E[4]100#100
(904) quinary-grangol = E[5]100#100
(905) senary-grangol = E[6]100#100
(907) duodecimal-grangol = E[12]100#100
(908) hexadecimal-grangol = E[16]100#100
(909) vigesimal-grangol = E[20]100#100
(910) sexagesimal-grangol = E[60]100#100
(911) centesimal-grangol = E[100]100#100 = E[100]1#101 = 100^^101
-logue section II
(912) monologialogue = E1#10 = 10^^10
(also (845) dekalogue)
(913) eyelash mite-logue = E1#20,000 = 10^^20,000
(914) dust mite-logue = E1#50,000 = 10^^50,000
(915) cheese mite-logue = E1#80,000 = 10^^80,000
(916) clover mite-logue = E1#200,000 = 10^^200,000
(917) pipsqueaklogue = E1#10,000,000 = 10^^10,000,000
(918) dialogialogue = E1#(10^10) = 10^^10^^2 = 10^^10,000,000,000
(919) squeakerlogue = E1#(5E10) = 10^^50,000,000,000
(920) small fry-logue = E1#(10^15)
(921) guppylogue = E1#(10^20)
(922) minnowlogue = E1#(10^25)
(923) gobylogue = E1#(10^35)
(924) gogologue = E1#(10^50)
(925) prawnlogue = E1#(10^65)
(926) lightweightlogue = E1#(10^75)
(927) ogologue = E1#(10^80)
(928) twerpuloidlogue = E1#(10^85)
(925) googologue ☆★ = E1#(10^100) = 10^^10^100
(926) guppylogiachime = E1#(10^200)
(927) ecetonlogue = E1#(10^303)
(928) googologiading = E1#(10^500)
(929) googologiachime = E1#(10^1000)
(930) googologiabell = E1#(10^5000)
(931) googologiatoll = E1#(10^10,000)
(932) googologiagong = E1#(10^100,000)
(933) milliplexionlogue = E1#(10^1,000,000)
(934) googologiabong = E1#(10^100,000,000)
(935) billiplexionlogue = E1#(10^10^9)
(936) trialogialogue = E1#(10^10^10) = 10^^10^^3 = 10^^10^10^10
(937) googologiathrong = E1#(10^10^11)
(938) trilliplexionlogue = E1#(10^10^12)
(939) googologiagandingan = E1#(10^10^14)
(940) guppyplexilogue = E1#(10^10^20)
(941) gogolplexilogue = E1#(10^10^50)
(942) googolplexilogue = E1#(10^10^100) = 10^^10^10^100
(943) googolplexilogiachime = E1#(10^10^1000)
(944) googolplexilogiatoll = E1#(10^10^10,000)
(945) googolplexilogiagong = E1#(10^10^100,000)
(946) milliduplexionlogue = E1#(10^10^1,000,000)
(947) tetralogialogue = E1#(10^10^10^10) = 10^^10^^4 = 10^^10^10^10^10
(948) guppyduplexilogue = E1#(10^10^10^20)
(949) googolduplexilogue = E1#(10^10^10^100)
(950) pentalogialogue = E1#(10^10^10^10^10) = 10^^10^^5
(951) googoltriplexilogue = E1#(10^10^10^10^100)
(952) hexalogialogue = E1#(E1#6) = E1#6#2 = 10^^10^^6
(953) heptalogialogue = E1#7#2 = 10^^10^^7
(954) octalogialogue = E1#8#2 = 10^^10^^8
(955) ennalogialogue = E1#9#2 = 10^^10^^9
(956) dekalogialogue = E1#10#2 = 10^^10^^10
...
(957) hectalogialogue = E1#100#2 = 10^^10^^100
(958) chilialogialogue = E1#1000#2 = 10^^10^^1000
(959) myrialogialogue = E1#10,000#2 = 10^^10^^10,000
(960) octadialogialogue = E1#100,000,000#2 = 10^^10^^100,000,000
(961) dialogialogialogue = E1#10,000,000,000#2 = 10^^10^^10,000,000,000
(962) sedeniadialogialogue = E1#10,000,000,000,000,000#2 = E1#(10^16)#2 = 10^^10^^10^16
(963) guppylogialogue = E1#(10^20)#2 = 10^^10^^10^20
(964) googologialogue = E1#(10^100)#2 = 10^^10^^10^100
(965) googologialogiagong = E1#(10^100,000)#2 = 10^^10^^10^100,000
(966) trialogialogialogue = E1#3#3 = 10^^10^^10^^3
(967) googolplexilogialogue = E1#(10^10^100)#2 = 10^^10^^10^10^100
(968) tetralogialogialogue = E1#4#3 = 10^^10^^10^^4
(969) pentalogialogialogue = E1#5#3 = 10^^10^^10^^5
(970) hexalogialogialogue = E1#6#3 = 10^^10^^10^^6
(971) heptalogialogialogue = E1#7#3 = 10^^10^^10^^7
(972) octalogialogialogue = E1#8#3 = 10^^10^^10^^8
(973) ennalogialogialogue = E1#9#3 = 10^^10^^10^^9
(974) dekalogialogialogue = E1#10#3 = 10^^10^^10^^10
...
(975) hectalogialogialogue = E1#100#3 = 10^^10^^10^^100
(976) chilialogialogialogue = E1#1000#3 = 10^^10^^10^^1000
(977) myrialogialogialogue = E1#10,000#3 = 10^^10^^10^^10,000
(978) octadialogialogialogue = E1#100,000,000#3 = 10^^10^^10^^100,000,000
(979) sedeniadialogialogialogue = E1#(10^16)#3 = 10^^10^^10^^10^16
...
(980) dialogialogialogialogue = E1#10,000,000,000 = 10^^10^^10^^10,000,000,000
(981) googologialogialogue = E1#(10^100)#3 = 10^^10^^10^^10^100
(982) trialogialogialogialogue = E1#3#4 = 10^^10^^10^^10^^3
(983) tetralogialogialogialogue = E1#4#4 = 10^^10^^10^^10^^4
(984) dekalogialogialogialogue = E1#10#4 = 10^^10^^10^^10^^10
(985) hectalogialogialogialogue = E1#100#4 = 10^^10^^10^^10^^100
... and something insane ...
(986) dekalogialogialogialogialogue = E1#10#5 = 10^^10^^10^^10^^10^^10 = 10^^^6
(987) dekalogialogialogialogialogialogue = E1#10#6 = 10^^10^^10^^10^^10^^10^^10 = 10^^^7
(988) dekalogialogialogialogialogialogialogue = E1#10#7 = 10^^10^^10^^10^^10^^10^^10^^10 = 10^^^8
(989) dekalogialogialogialogialogialogialogialogue = E1#10#8 = 10^^10^^10^^10^^10^^10^^10^^10^^10 = 10^^^9
(990) dekalogialogialogialogialogialogialogialogialogue ✡ = E1#10#9 = 10^^10^^10^^10^^10^^10^^10^^10^^10^^10 = 10^^^10
Oh my god! That number is so long and crazy! Just repeat "-logue"s to make them even more insane!
-dex section
... at this point the constant nesting of the -logue operator becomes difficult to read and say. What would be even better? If we could get the same recursion with our new grangol number. We can have a grangol 10's with a determinant of 100, or the grangolth member of the googol series. We can't use "plex" here. If we use the definition we established in the "googol series" that means 10^n. Technically we would have to say:
(991) grangolplex = E(E100#100) = E100#101
... then something similar like...
(992) grangolduplex = E(E100#100)#2 = E(E100#101)#1 = E100#102
(993) grangoltriplex = E(E100#100)#3 = E100#103
...
(994) grangoldeciplex = E(E100#100)#10 = E100#110
We can see that E(Ea#b)#c = Ea#(b+c), by the rule Ea#b = E(Ea#(b-1)).
Therefore I suggest a new prefix, called "dex". The "dex" simply takes the number, and substitutes it back into the replicator. Basically the "dex" function generates a power tower with a height equal to it's input! We can then define the following numbers:
(995) grangoldex ☆★ = E100#100#2 = E100#(E100#100) = E100#grangol =
EEEEEE ... ... ... ... ... ... EEEEEE100 (w/grangol "E"s) =
10^10^10^ ... ... ... ... ^10^10^10^100 (w/grangol 10s)
... moving on ...
(996) grangoldudex ☆★ = E100#100#3 = E100#(E100#100#2) = E100#grangoldex
(997) grangoltridex ☆★ = E100#100#4 = E100#(E100#100#3) = E100#grangoldudex
(998) grangolquadridex ☆ = E100#100#5 = E100#(E100#100#4) = E100#grangoltridex
(999) grangolquintidex ☆ = E100#100#6 = E100#(E100#100#5) = E100#grangolquadridex
(1000) grangolsextidex = E100#100#7
(1001) grangolseptidex = E100#100#8
(1002) grangoloctidex = E100#100#9
(1003) grangolnonidex = E100#100#10
(1004) grangoldecidex = E100#100#11
...
(1005) grangolvigintidex = E100#100#21
...
(1006) grangolcentidex = E100#100#101
(1007) grangolmillidex = E100#100#1001
(1008) grangolmilli-millidex = E100#100#1,000,001
... and even ...
(1009) grangol-grangolidex ✡ = E100#100#(E100#100+1)
The ability to mix suffixes allows us to name many inbetween values which exist between the Grangol Series. The following series exists entirely between a grangol and a grangoldex:
(1010) googoldex ☆★ = E100#1#2 = E100#(E100) = E100#googol = 10^10^10^...^10^10^100 (w/googol 10s)
(1011) googolplexidex ☆★ = E100#2#2 = E100#(E100#2) = E100#googolplex
(1012) googolduplexidex = E100#3#2 = E100#(E100#3) = E100#googolduplex
(1013) googoltriplexidex = E100#4#2 = E100#(E100#4) = E100#googoltriplex
(1014) googolquadriplexidex = E100#5#2 = E100#(E100#5) = E100#googolquadriplex
(1015) googolquintiplexidex = E100#6#2 = E100#(E100#6) = E100#googolquintiplex
(1016) googolsextiplexidex = E100#7#2 = E100#(E100#7) = E100#googolsextiplex
(1017) googolseptiplexidex = E100#8#2 = E100#(E100#8) = E100#googolseptiplex
(1018) googoloctiplexidex = E100#9#2 = E100#(E100#9) = E100#googoloctiplex
(1019) googolnoniplexidex = E100#10#2 = E100#(E100#10) = E100#googolnoniplex
(1020) googoldeciplexidex = E100#11#2 = E100#(E100#11) = E100#googoldeciplex
...
(1021) googolcentiplexidex = E100#101#2 = E100#(E100#101) = E100#googolcentiplex
We can also use the "dex" and "plex" suffixes in non-standard ways to create even more numbers. Whenever converting a name involving mixed types of suffixes, apply the suffixes from left to right. Here are some examples:
(1022) googolplexidexiplex = E100#(1+E100#2)
(1023) googolplexidexiduplex = E100#(2+E100#2)
(1024) googoldexiplex = E(E100#1#2) = E(E100#(E100)) = E(E100#(E100)) = E100#((E100)+1)
(1025) googoldexiduplex = E(E100#1#2)#2 = E(E100#(E100))#2 = E100#((E100)+2)
(1026) googoldexitriplex = E(E100#1#2)#3 = E(E100#(E100))#3 = E100#((E100)+3)
... and something crazy ...
(1027) grangolplexidex = E100#101#2 = E100#(E100#101)
(also (1021) googolcentiplexidex)
We can also create a series which will fall between a grangoldex and a grangoldudex:
(1028) googoldudex = E100#1#3 = E100#(E100#1#2) = E100#(E100#(E100)) = E100#(E100#googol)
(1029) googolplexidudex = E100#2#3
(1030) googolduplexidudex = E100#3#3
(1031) googoltriplexidudex = E100#4#3
(1032) googolquadriplexidudex = E100#5#3
(1033) googolquintiplexidudex = E100#6#3
(1034) googolsextiplexidudex = E100#7#3
(1035) googolseptiplexidudex = E100#8#3
(1036) googoloctiplexidudex = E100#9#3
(1037) googolnoniplexidudex = E100#10#3
(1038) googoldeciplexidudex = E100#11#3
etc.
We can keep going in this manner with even more in between values...
( between grangoldudex and grangoltridex )
(1039) googoltridex = E100#1#4
(1040) googolplexitridex = E100#2#4
(1041) googolduplexitridex = E100#3#4
(1042) googoltriplexitridex = E100#4#4
(1043) googolquadriplexitridex = E100#5#4
(1044) googolquintiplexitridex = E100#6#4
...
( between grangoltridex and grangolquadridex )
(1045) googolquadridex = E100#1#5
(1046) googolplexiquadridex = E100#2#5
(1047) googolduplexiquadridex = E100#3#5
...
( between grangolquadridex and grangolquintidex )
(1048) googolquintidex = E100#1#6
(1049) googolplexiquintidex = E100#2#6
(1050) googolduplexiquintidex = E100#3#6
...
( between grangolquintidex and grangolsextidex )
(1051) googolsextidex = E100#1#7
(1052) googolplexisextidex = E100#2#7
(1053) googolduplexisextidex = E100#3#7
...
( between grangolsextidex and grangolseptidex )
(1054) googolseptidex = E100#1#8
(1055) googolplexiseptidex = E100#2#8
(1056) googolduplexiseptidex = E100#3#8
...
( between grangolseptidex and grangoloctidex )
(1057) googoloctidex = E100#1#9
(1058) googolplexioctidex = E100#2#9
(1059) googolduplexioctidex = E100#3#9
...
( between grangoloctidex and grangolnonidex )
(1060) googolnonidex = E100#1#10
(1061) googolplexinonidex = E100#2#10
(1062) googolduplexinonidex = E100#3#10
...
( between grangolnonidex and grangoldecidex )
(1063) googoldecidex = E100#1#11
(1064) googolplexidecidex = E100#2#11
(1065) googolduplexidecidex = E100#3#11
That's quite a lot of googolism's we can form already, but we aren't done yet.
Power modifier section II
We can also apply the suffixes -chime, -toll , -gong , -bong, and -throng to a grangol as well.
Here is some of the members of the Grangolchime Series:
(1066) grangolchime = E1000#1000
= 10^10^10^10^ ... ... ... ... ^10^10^10^10^1000 (w/1000 tens)
(1067) grangoldexichime = E1000#1000#2
(1068) grangoldudexichime = E1000#1000#3
(1069) grangoltridexichime = E1000#1000#4
(1070) grangolquadridexichime = E1000#1000#5
(1071) grangolquintidexichime = E1000#1000#6
(1072) grangolsextidexichime = E1000#1000#7
(1073) grangolseptidexichime = E1000#1000#8
(1074) grangoloctidexichime = E1000#1000#9
(1075) grangolnonidexichime = E1000#1000#10
(1076) grangoldecidexichime = E1000#1000#11
Now we create a Grangoltoll Series:
(1077) grangoltoll = E10,000#10,000
= 10^10^10^10^ ... ... ... ... ^10^10^10^10^10,000 (w/10,000 tens)
(1078) grangoldexitoll = E10,000#10,000#2
(1079) grangoldudexitoll = E10,000#10,000#3
(1081) grangoltridexitoll = E10,000#10,000#4
(1082) grangolquadridexitoll = E10,000#10,000#5
(1083) grangolquintidexitoll = E10,000#10,000#6
(1084) grangolsextidexitoll = E10,000#10,000#7
(1085) grangolseptidexitoll = E10,000#10,000#8
(1086) grangoloctidexitoll = E10,000#10,000#9
(1087) grangolnonidexitoll = E10,000#10,000#10
(1088) grangoldecidexitoll = E10,000#10,000#11
Of course we can also have a Grangolgong Series as well:
(1089) grangolgong ☆ = E100,000#100,000 = 10^10^ ... ... ^10^10^100,000 (w/100,000 tens)
(1090) grangoldexigong ☆ = E100,000#100,000#2 = E100,000#grangolgong
(1091) grangoldudexigong = E100,000#100,000#3 = E100,000#grangoldexigong
(1092) grangoltridexigong = E100,000#100,000#4 = E100,000#grangoldudexigong
(1093) grangolquadridexigong = E100,000#100,000#5 = E100,000#grangoltridexigong
(1094) grangolquintidexigong = E100,000#100,000#6 = E100,000#grangolquadridexigong
(1095) grangolsextidexigong = E100,000#100,000#7
(1096) grangolseptidexigong = E100,000#100,000#8
(1097) grangoloctidexigong = E100,000#100,000#9
(1098) grangolnonidexigong = E100,000#100,000#10
(1099) grangoldecidexigong = E100,000#100,000#11
...
(1100) grangolvigintidexigong = E100,000#100,000#21
(1101) grangolcentidexigong = E100,000#100,000#101
(1102) grangolmillidexigong = E100,000#100,000#1001
(1103) grangolmilli-millidexigong = E100,000#100,000#1,000,001
We can also introduce the grangolbong and grangolthrong series as well:
(1104) grangolbong = E100,000,000#100,000,000
(1105) grangoldexibong = E100,000,000#100,000,000#2
(1106) grangoldudexibong = E100,000,000#100,000,000#3
etc.
(1107) grangolthrong = E100,000,000,000#100,000,000,000
(1108) grangoldexithrong = E100,000,000,000#100,000,000,000#2
(1109) grangoldudexithrong = E100,000,000,000#100,000,000,000#3
There is another problem! Saibian conclude that remainders of size modifiers (-speck, -crumb, -chunk, -bunch, -crowd, -swarm) and power modifiers (-ding, -bell, -gandingan) will not be used beyond guppy regiment.
So, to continue, I am going to introduce remainder of argument modifiers, using the similar reasoning that grangolgong is defined as E100,000#100,000, using power modifier root that applies to all arguments which replaces 100 with 100,000. First, we introduce -ding, -bell, and -gandingan.
(1110) grangolding = E500#500
(1111) grangoldexiding = E500#500#2
(1112) grangoldudexiding = E500#500#3
etc.
(1113) grangolbell = E5000#5000
(1114) grangoldexibell = E5000#5000#2
(1115) grangoldudexibell = E5000#5000#3
etc.
(1116) grangolgandingan = E100,000,000,000,000#100,000,000,000,000
(1117) grangoldexigandingan = E100,000,000,000,000#100,000,000,000,000#2
(1118) grangoldudexigandingan = E100,000,000,000,000#100,000,000,000,000#3
How about size modifiers? Let see that:
googolspeck = E90 = 10^90
googolcrumb = E95 = 10^95
googolchunk = E99 = 10^99
googolbunch = E101 = 10^101
googolcrowd = E105 = 10^105
googolswarm = E110 = 10^110
So,
(1119) grangolspeck = E90#90
(1120) grangolcrumb = E95#95
(1121) grangolchunk = E99#99
(1122) grangolbunch = E101#101
(1123) grangolcrowd = E105#105
(1124) grangolswarm = E110#110
We can also apply our suffixes to other numbers besides a grangol. Here's what happens when we apply them to Jonathan Bowers' giggol:
(1125) giggolding = E1#500 = 10^^500
(1126) giggolchime = E1#1000 = 10^^1000 = 10^10^...^10^10 w/1000 10s
(1127) giggolbell = E1#5000 = 10^^5000
(1128) giggoltoll = E1#10,000 = 10^^10,000 = 10^10^...^10^10 w/10,000 10s
(1129) giggolgong = E1#100,000 = 10^^100,000 = 10^10^...^10^10 w/100,000 10s
(1130) giggolbong = E1#100,000,000
(1131) giggolthrong = E1#100,000,000,000
(1132) giggolgandingan = E1#100,000,000,000,000
...
(1133) giggolspeck = E1#90
(1134) giggolcrumb = E1#95
(1135) giggolchunk = E1#99
(1136) giggolbunch = E1#101
(1137) giggolcrowd = E1#105
(1138) giggolswarm = E1#110
We can see that:
hectalogue < giggolbunch < grangol < grangolplex < grangolbunch
Eceton section II
For extending the centillion into this range we can use these names:
(1139) ecetondex ☆ = E303#1#2 = E303#(E303) = E303#centillion
= 10^10^10^ ... ... ^10^10^303 (w/centillion tens!)
(1140) ecetondudex ☆ = E303#1#3 = E303#ecetondex
(1141) ecetontridex = E303#1#4 = E303#ecetondudex
(1142) ecetonquadridex = E303#1#5 = E303#ecetontridex
(1143) ecetonquintidex = E303#1#6 = E303#ecetonquadridex
(1144) ecetonsextidex = E303#1#7
(1145) ecetonseptidex = E303#1#8
(1146) ecetonoctidex = E303#1#9
(1147) ecetonnonidex = E303#1#10
(1148) ecetondecidex = E303#1#11
...
(1149) ecetoncentidex = E303#1#101
(1150) ecetonmillidex = E303#1#1,001
(1151) ecetonmilli-millidex = E303#1#1,000,001
(1152) eceton-ecetonidex = E303#1#(E303+1)
(1153) eceton-ecetonplexiadex = E303#1#(E303#2+1) = E303#1#(EE303+1)
(1154) eceton-ecetondexiadex = E303#1#(E303#1#2+1)
Of course, we can mix -plex and -dex to eceton like:
(1155) ecetonplexidex = E303#2#2 = E303#(E303#2) = E303#(EE303) = E303#ecetonplex
(1156) ecetonduplexidex = E303#3#2
(1157) ecetontriplexidex = E303#4#2
(1158) ecetonquadriplexidex = E303#5#2
(1159) ecetonquintiplexidex = E303#6#2
...
(1160) ecetonplexidudex = E303#2#3
(1161) ecetonduplexidudex = E303#3#3
(1162) ecetontriplexidudex = E303#4#3
...
(1163) ecetonplexitridex = E303#2#4
(1164) ecetonduplexitridex = E303#3#4
(1165) ecetontriplexitridex = E303#4#4
We can also have ecetonate versions of the respective numbers, but with 303 in the second argument of the Hyper-E notation instead of 1, 2, 3, 4, ...
We have:
(899) eceto-grangol = E303#303
So we have:
(1166) eceto-grangoldex = E303#303#2
(1167) eceto-grangoldudex = E303#303#3
(1168) eceto-grangoltridex = E303#303#4
(1169) eceto-grangolquadridex = E303#303#5
(1170) eceto-grangolquintidex = E303#303#6
(1171) eceto-grangolsextidex = E303#303#7
(1172) eceto-grangolseptidex = E303#303#8
(1173) eceto-grangoloctidex = E303#303#9
(1174) eceto-grangolnonidex = E303#303#10
(1175) eceto-grangoldecidex = E303#303#11
And something insane like:
(1176) eceto-grangolplex = E(E303#303) = E303#304
-taxis section
(1177) tria-taxis ⍟☆★ = E1#1#3 = E1#(E1#10) = E1#dekalogue = 10^^^3 = 10^^10^^10
(old: tria-teraksys)
(1178) tetra-taxis ⍟☆★ = E1#1#4 = E1#(E1#(E1#10)) = E1#tria-taxis = 10^^^4 = 10^^10^^10^^10
(old: tetra-teraksys)
(1179) penta-taxis ⍟☆ = E1#1#5 = E1#(E1#(E1#(E1#10))) = E1#tetra-taxis = 10^^^5
(old: penta-teraksys)
(1180) hexa-taxis ⍟☆ = E1#1#6 = E1#(E1#(E1#(E1#(E1#10)))) = E1#penta-taxis = 10^^^6
(old: hexa-teraksys)
(1181) hepta-taxis ⍟☆ = E1#1#7 = E1#hexa-taxis = 10^^^7
(old: hepta-teraksys)
(1182) octa-taxis ⍟☆ = E1#1#8 = E1#hepta-taxis = 10^^^8
(old: octa-teraksys)
(1183) enna-taxis ⍟☆ = E1#1#9 = E1#octa-taxis = 10^^^9
(old: enna-teraksys)
(1184) deka-taxis ⍟☆★ = E1#1#10 = E1#enna-taxis = 10^^^10
(old: deka-teraksys)
(1185) endeka-taxis = E1#1#11 = 10^^^11
(1186) dodeka-taxis = E1#1#12 = 10^^^12
(1187) triadeka-taxis = E1#1#13 = 10^^^13
(1188) tetradeka-taxis = E1#1#14 = 10^^^14
(1189) pentadeka-taxis = E1#1#15 = 10^^^15
(1190) hexadeka-taxis = E1#1#16 = 10^^^16
(1191) heptadeka-taxis = E1#1#17 = 10^^^17
(1192) octadeka-taxis = E1#1#18 = 10^^^18
(1193) ennadeka-taxis = E1#1#19 = 10^^^19
(1194) icosa-taxis = E1#1#20 = 10^^^20
...
(1195) trianta-taxis = E1#1#30 = 10^^^30
(1196) teranta-taxis = E1#1#40 = 10^^^40
(1197) penanta-taxis = E1#1#50 = 10^^^50
(1198) exata-taxis = E1#1#60 = 10^^^60
(1199) eptata-taxis = E1#1#70 = 10^^^70
(1200) ogdata-taxis = E1#1#80 = 10^^^80
(1201) entata-taxis = E1#1#90 = 10^^^90
...
(1202) hecta-taxis ⍟☆★ = E1#1#100 (old: hecta-teraksys)
Hecta-taxis is equivalent to 10^^^100, which is known as "gaggol" in Bowers system. Furthermore we may introduce...
(1203) dohecta-taxis = E1#1#200
(1204) triahecta-taxis = E1#1#300
(1205) tetrahecta-taxis = E1#1#400
(1206) pentahecta-taxis = E1#1#500
(1207) hexahecta-taxis = E1#1#600
(1208) heptahecta-taxis = E1#1#700
(1209) octahecta-taxis = E1#1#800
(1210) ennahecta-taxis = E1#1#900
(1211) chilia-taxis = E1#1#1000
(1212) myria-taxis = E1#1#10,000
(1213) hecta-chilia-taxis = E1#1#100,000
(1214) chilia-chilia-taxis = E1#1#1,000,000
(1215) chilia-myria-taxis = E1#1#10,000,000
(1216) myria-myria-taxis = E1#1#100,000,000
alternatively...
(1217) octadia-taxis = E1#1#100,000,000
furthermore...
(1218) sedeniadia-taxis = E1#1#(10^16) = E1#1#10,000,000,000,000,000
...
(1219) dialogia-taxis = E1#1#10,000,000,000
(1220) guppia-taxis = E1#1#(10^20)
(1221) minnowia-taxis = E1#1#(10^25)
(1222) gobia-taxis = E1#1#(10^35)
(1223) gogolia-taxis = E1#1#(10^50)
(1224) ogolia-taxis = E1#1#(10^80)
(1225) googolia-taxis = E1#1#(10^100) = 10^^^10^100
(1226) googoldingia-taxis = E1#1#(10^500)
(1227) googolchimia-taxis = E1#1#(10^1000)
(1228) googolbellia-taxis = E1#1#(10^5000)
(1229) googoltollia-taxis = E1#1#(10^10,000)
(1230) googolgongia-taxis = E1#1#(10^100,000)
(1231) milliplexionia-taxis = E1#1#(10^1,000,000)
(1232) googolbongia-taxis = E1#1#(10^100,000,000)
(1233) billiplexionia-taxis = E1#1#(10^10^9)
(1234) trialogia-taxis = E1#1#(10^10^10) = 10^^^10^10^10
(1235) googolthrongia-taxis = E1#1#(10^10^11)
(1236) trilliplexionia-taxis = E1#1#(10^10^12)
(1237) googolgandingia-taxis = E1#1#(10^10^14)
(1238) guppyplexia-taxis = E1#1#(10^10^20)
(1239) googolplexia-taxis = E1#1#(10^10^100) = 10^^^10^10^100
(1240) googolplexichimia-taxis = E1#1#(10^10^1000) = 10^^^10^10^1000
(1241) googolplexitollia-taxis = E1#1#(10^10^10,000) = 10^^^10^10^10,000
(1242) googolplexigongia-taxis = E1#1#(10^10^100,000) = 10^^^10^10^100,000
(1243) milliduplexionia-taxis = E1#1#(10^10^1,000,000) = 10^^^10^10^1,000,000
(1245) tetralogia-taxis = E1#1#(10^10^10^10) = 10^^^10^10^10^10
(1246) googolduplexia-taxis = E1#1#(10^10^10^100) = 10^^^10^10^100
(1247) googolduplexigongia-taxis = E1#1#(10^10^10^100,000) = 10^^^10^10^100,000
(1248) pentalogia-taxis = E1#1#(10^10^10^10^10) = 10^^^10^10^10^10^10
(1249) googoltriplexia-taxis = E1#1#(10^10^10^10^100) = 10^^^10^10^10^10^100
(1250) hexalogia-taxis = E1#1#(E1#6) = 10^^^10^^6
(1251) heptalogia-taxis = E1#1#(E1#7) = 10^^^10^^7
(1252) octalogia-taxis = E1#1#(E1#8) = 10^^^10^^8
(1253) ennalogia-taxis = E1#1#(E1#9) = 10^^^10^^9
(1254) dekalogia-taxis = E1#1#(E1#10) = 10^^^10^^10 = 10^^^10^^^2
(1255) hectalogia-taxis = E1#1#(E1#100) = 10^^^10^^100
(1256) triataxia-taxis = E1#1#(E1#1#3) = E1#1#3#2 = 10^^^10^^^3
(1257) tetrataxis-taxis = E1#1#(E1#1#4) = E1#1#4#2 = 10^^^10^^^4
(1258) dekataxia-taxis = E1#1#10#2 = E1#1#1#3 = 10^^^10^^^10 = 10^^^^3
(1259) hectataxia-taxis = E1#1#100#2 = 10^^^10^^^100
(1260) triataxiataxia-taxis = E1#1#3#3 = 10^^^10^^^10^^^3
(1261) dekataxiataxia-taxis = E1#1#10#3 = E1#1#1#4 = 10^^^10^^^10^^^10 = 10^^^^4
(1262) hectataxiataxia-taxis = E1#1#100#3 = 10^^^10^^^10^^^100
(1263) dekataxiataxiataxia-taxis = E1#1#10#4 = E1#1#1#5 = 10^^^10^^^10^^^10^^^10 = 10^^^^5
(1264) hectataxiataxiataxia-taxis = E1#1#100#4 = 10^^^10^^^10^^^10^^^100
(1265) dekataxiataxiataxiataxia-taxis ✡ = E1#1#10#5 = E1#1#1#6 = 10^^^10^^^10^^^10^^^10^^^10 = 10^^^^6
At this point we've already far surpassed anything we encountered in chapter E4, and we've just begun! Let's now continue to the next level...