Category 7
Regiment block 9
Members: 68 (46 original + 22 new)
(1923 - 1990)
[7 arrows to 8 arrows]
Level 1 | Stage 2-4
Stage 2-4 ~ Breaking gigantic googol of the intermediate up-arrow notation level.
Due to the popularity of my extension of the classic googol-series, some have tried to extend it beyond the Gulgol group. In response to this I created the 7th group of the main series: the Gaspgol Regiment (the gaspgol is short for the *gasp* googol), and the 8th, the Ginorgol Regiment.
Predictably the gaspgol is defined as:
(1923) gaspgol ☆★ = E100#100#100#100#100#100#100
(Note: the gaspgol is comparable to and slightly greater than the "gagol" of Bowers' System)
We can also have:
(1924) gaspgolheptex = E100#100#100#100#100#100#100#2
(1925) gaspgolduheptex = E100#100#100#100#100#100#100#3
(1926) gaspgoltriheptex = E100#100#100#100#100#100#100#4
etc.
Applying our modifiers we also have...
(1927) gaspgolding = E500#500#500#500#500#500#500
etc.
(1928) gaspgolchime = E1000#1000#1000#1000#1000#1000#1000
(1929) gaspgolheptexichime = E1000#1000#1000#1000#1000#1000#1000#2
(1930) gaspgolduheptexichime = E1000#1000#1000#1000#1000#1000#1000#3
etc.
(1931) gaspgolbell = E5000#5000#5000#5000#5000#5000#5000
etc.
(1932) gaspgoltoll = E10,000#10,000#10,000#10,000#10,000#10,000#10,000
(1933) gaspgolheptexitoll = E10,000#10,000#10,000#10,000#10,000#10,000#10,000#2
(1934) gaspgolduheptexitoll = E10,000#10,000#10,000#10,000#10,000#10,000#10,000#3
etc.
(1935) gaspgolgong = E100,000#100,000#100,000#100,000#100,000#100,000#100,000
(1936) gaspgolheptexigong = E100,000#100,000#100,000#100,000#100,000#100,000#100,000#2
(1937) gaspgolduheptexigong = E100,000#100,000#100,000#100,000#100,000#100,000#100,000#3
etc.
(1938) gaspgolbong
= E100,000,000#100,000,000#100,000,000#100,000,000#100,000,000#100,000,000#100,000,000
(1939) gaspgolheptexibong
= E100,000,000#100,000,000#100,000,000#100,000,000#100,000,000#100,000,000#100,000,000#2
etc.
(1940) gaspgolthrong
= E100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000
(1941) gaspgolheptexithrong
= E100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#2
etc.
(1942) gaspgolgandingan =
E100,000,000,000,000#100,000,000,000,000#100,000,000,000,000#100,000,000,000,000#
100,000,000,000,000#100,000,000,000,000#100,000,000,000,000
etc.
We can also apply our suffixes to Bowers' gagol:
(1943) gagolding = E1#1#1#1#1#1#500
(1944) gagolchime = E1#1#1#1#1#1#1000
(1945) gagolbell = E1#1#1#1#1#1#5000
(1946) gagoltoll = E1#1#1#1#1#1#10,000
(1947) gagolgong = E1#1#1#1#1#1#100,000
(1948) gagolbong = E1#1#1#1#1#1#100,000,000
(1949) gagolthrong = E1#1#1#1#1#1#100,000,000,000
(1950) gagolgandingan = E1#1#1#1#1#1#100,000,000,000,000
Revise back a regiment behind! Let's define the missing googolism based on combinatory:
(1951) gulgolcentihex = E100#100#100#100#100#100#101
(also (1767) gorgegolcentipentex. Belongs to the gulgol regiment.)
(1952) gaspgolcentiheptex = E100#100#100#100#100#100#100#101
Next the combinatorial googolism's:
(1953) googolheptex = E100#1#1#1#1#1#1#2
(1954) grangolheptex = E100#100#1#1#1#1#1#2
(1955) greagolheptex = E100#100#100#1#1#1#1#2
(1956) gigangolheptex = E100#100#100#100#1#1#1#2
(1957) gorgegolheptex = E100#100#100#100#100#1#1#2
etc.
(1958) gaspgolplex = E(E100#100#100#100#100#100#100)
(1959) gaspgoldex = E100#(E100#100#100#100#100#100#100)
(1960) gaspgolthrex = E100#100#(E100#100#100#100#100#100#100)
(1961) gaspgoltetrex = E100#100#100#(E100#100#100#100#100#100#100)
(1962) gaspgolpentex = E100#100#100#100#(E100#100#100#100#100#100#100)
(1963) gaspgolhex = E100#100#100#100#100#(E100#100#100#100#100#100#100)
= E100#100#100#100#100#100#101
Next the in betweens...
(1964) gulgolheptex = E100#100#100#100#100#100#1#2
(1965) gulgolhexiheptex = E100#100#100#100#100#100#2#2
(1966) gulgolduhexiheptex = E100#100#100#100#100#100#3#2
etc.
between gaspgolheptex and gaspgolduheptex ...
(1967) gulgolduheptex = E100#100#100#100#100#100#1#3
(1968) gulgolhexiduheptex = E100#100#100#100#100#100#2#3
(1969) gulgolduhexiduheptex = E100#100#100#100#100#100#3#3
etc.
Next the ecetonheptex series:
(1970) ecetonheptex = E303#1#1#1#1#1#1#2
(1971) ecetonduheptex = E303#1#1#1#1#1#1#3
etc.
(1972) eceto-gaspgol = E303#303#303#303#303#303#303
(1973) eceto-gaspgolheptex = E303#303#303#303#303#303#303#2
(1974) eceto-gaspgolduheptex = E303#303#303#303#303#303#303#3
etc.
You could have a little bit weird:
(1975) gaspgoldingplex = E(E500#500#500#500#500#500#500)
Lastly the -ennaxis series...
(1976) tria-ennaxis ⍟☆ = E1#1#1#1#1#1#1#3 = 10^^^^^^^^3
(formerly tria-ennaksys)
(1977) tetra-ennaxis ⍟☆ = E1#1#1#1#1#1#1#4 = 10^^^^^^^^4
(formerly tetra-ennaksys)
(1978) penta-ennaxis ⍟ = E1#1#1#1#1#1#1#5 = 10^^^^^^^^5
(1979) hexa-ennaxis ⍟ = E1#1#1#1#1#1#1#6 = 10^^^^^^^^6
(1980) hepta-ennaxis ⍟ = E1#1#1#1#1#1#1#7 = 10^^^^^^^^7
(1981) octa-ennaxis ⍟ = E1#1#1#1#1#1#1#8 = 10^^^^^^^^8
(1982) enna-ennaxis ⍟ = E1#1#1#1#1#1#1#9 = 10^^^^^^^^9
(1983) deka-ennaxis ⍟☆ = E1#1#1#1#1#1#1#10 = 10^^^^^^^^10
(formerly deka-ennaksys)
...
(1984) icosa-ennaxis ⍟☆ = E1#1#1#1#1#1#1#20 = 10^^^^^^^^20
(1985) hecta-ennaxis ⍟☆ = E1#1#1#1#1#1#1#100 = 10^^^^^^^^100
(formerly hecta-ennaksys)
The deka-ennaxis is equivalent to 10^^^^^^^^10. This is equal to the small "tridecal" (tridecal Jr.) of Bowers' old System. We can also have...
(1986) chilia-ennaxis = E1#1#1#1#1#1#1#1000 = 10^^^^^^^^1000
(1987) myria-ennaxis = E1#1#1#1#1#1#1#10,000 = 10^^^^^^^^10,000
(1988) octadia-ennaxis = E1#1#1#1#1#1#1#100,000,000
(1989) sedeniadia-ennaxis = E1#1#1#1#1#1#1#10,000,000,000,000,000
And finally,
(1990) deka-ennaxia-ennaxis ✡ = E1#1#1#1#1#1#1#10#2
Category 8
Regiment block 10
Members: 60 (43 original + 17 new)
(1991 - 2050)
[8 arrows to 9 arrows]
Due to the popularity of my extension of the classic googol-series, some have tried to extend it beyond the Gulgol group. In response to this I created the 7th group of the main series: the Gaspgol Regiment (the gaspgol is short for the *gasp* googol), and the 8th, the Ginorgol Regiment.
Next is the Ginorgol Regiment (ginorgol is short for ginormous googol):
(1991) ginorgol ☆★ = E100#100#100#100#100#100#100#100
We can also have:
(1992) ginorgoloctex = E100#100#100#100#100#100#100#100#2
(1993) ginorgolduoctex = E100#100#100#100#100#100#100#100#3
(1994) ginorgoltrioctex = E100#100#100#100#100#100#100#100#4
...
(1995) ginorgolcentioctex = E100#100#100#100#100#100#100#100#101
etc.
... now applying our suffixes we get...
(1996) ginorgolding = E500#500#500#500#500#500#500#500
etc.
(1997) ginorgolchime = E1000#1000#1000#1000#1000#1000#1000#1000
(1998) ginorgoloctexichime = E1000#1000#1000#1000#1000#1000#1000#1000#2
(1999) ginorgolduoctexichime = E1000#1000#1000#1000#1000#1000#1000#1000#3
etc.
(2000) ginorgolbell = E5000#5000#5000#5000#5000#5000#5000#5000
etc.
(2001) ginorgoltoll = E10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000
(2002) ginorgoloctexitoll = E10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#2
(2003) ginorgolduoctexitoll = E10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#3
etc.
(2004) ginorgolgong = E100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000
(2005) ginorgoloctexigong = E100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#2
(2006) ginorgolduoctexigong = E100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#3
etc.
(2007) ginorgolbong
= E100,000,000#100,000,000#100,000,000#100,000,000#
100,000,000#100,000,000#100,000,000#100,000,000
(2008) ginorgoloctexibong
= E100,000,000#100,000,000#100,000,000#100,000,000#
100,000,000#100,000,000#100,000,000#100,000,000#2
etc.
(2009) ginorgolthrong
= E100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#
100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000
(2010) ginorgoloctexithrong
= E100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#
100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#2
etc.
(2011) ginorgolgandingan
= E100,000,000,000,000#100,000,000,000,000#100,000,000,000,000#100,000,000,000,000#
100,000,000,000,000#100,000,000,000,000#100,000,000,000,000#100,000,000,000,000
etc.
next are the combinatorial googolism's...
(2012) googoloctex = E100#1#1#1#1#1#1#1#2
(2013) grangoloctex = E100#100#1#1#1#1#1#1#2
(2014) greagoloctex = E100#100#100#1#1#1#1#1#2
(2015) gigangoloctex = E100#100#100#100#1#1#1#1#2
(2016) gorgegoloctex = E100#100#100#100#100#1#1#1#2
(2017) gulgoloctex = E100#100#100#100#100#100#1#1#2
also...
(2018) ginorgolplex = E(E100#100#100#100#100#100#100#100)
(2019) ginorgoldex = E100#(E100#100#100#100#100#100#100#100)
(2020) ginorgolthrex = E100#100#(E100#100#100#100#100#100#100#100)
(2021) ginorgoltetrex = E100#100#100#(E100#100#100#100#100#100#100#100)
(2022) ginorgolpentex = E100#100#100#100#(E100#100#100#100#100#100#100#100)
(2023) ginorgolhex = E100#100#100#100#100#(E100#100#100#100#100#100#100#100)
(2024) ginorgolheptex = E100#100#100#100#100#100#(E100#100#100#100#100#100#100#100)
= E100#100#100#100#100#100#100#101
...
Next the in-betweens...
in-between a ginorgol and a ginorgoloctex ...
(2025) gaspgoloctex = E100#100#100#100#100#100#100#1#2
(2026) gaspgolheptexioctex = E100#100#100#100#100#100#100#2#2
(2027) gaspgolduheptexioctex = E100#100#100#100#100#100#100#3#2
...
in-between a ginorgoloctex and a ginorgolduoctex ...
(2028) gaspgolduoctex = E100#100#100#100#100#100#100#1#3
(2029) gaspgolheptexiduoctex = E100#100#100#100#100#100#100#2#3
(2030) gaspgolduheptexiduoctex = E100#100#100#100#100#100#100#3#3
etc.
Next the ecetonoctex series ...
(2031) ecetonoctex = E303#1#1#1#1#1#1#1#2
(2032) ecetonduoctex = E303#1#1#1#1#1#1#1#3
etc.
(2033) eceto-ginorgol = E303#303#303#303#303#303#303#303
(2034) eceto-ginorgoloctex = E303#303#303#303#303#303#303#303#2
(2035) eceto-ginorgolduoctex = E303#303#303#303#303#303#303#303#3
Lastly the -dekaxis series ...
(2036) tria-dekaxis ⍟☆ = E1#1#1#1#1#1#1#1#3 = 10^^^^^^^^^3
(formerly tria-dekaksys)
(2037) tetra-dekaxis ⍟ = E1#1#1#1#1#1#1#1#4 = 10^^^^^^^^^4
(formerly tetra-dekaksys)
(2038) penta-dekaxis ⍟ = E1#1#1#1#1#1#1#1#5 = 10^^^^^^^^^5
(2039) hexa-dekaxis ⍟ = E1#1#1#1#1#1#1#1#6 = 10^^^^^^^^^6
(2040) hepta-dekaxis ⍟ = E1#1#1#1#1#1#1#1#7 = 10^^^^^^^^^7
(2041) octa-dekaxis ⍟ = E1#1#1#1#1#1#1#1#8 = 10^^^^^^^^^8
(2042) enna-dekaxis ⍟ = E1#1#1#1#1#1#1#1#9 = 10^^^^^^^^^9
(2043) deka-dekaxis ⍟☆ = E1#1#1#1#1#1#1#1#10 = 10^^^^^^^^^10
(formerly deka-dekaksys)
But be careful! Deka-dekaxis is not the same as tridecal! This is because the -taxis series has one arrow less.
...
(2044) icosa-dekaxis = E1#1#1#1#1#1#1#1#20 = 10^^^^^^^^^20
(2045) hecta-dekaxis ⍟☆ = E1#1#1#1#1#1#1#1#100 = 10^^^^^^^^^100
(formerly hecta-dekaksys)
...
(2046) chilia-dekaxis = E1#1#1#1#1#1#1#1#1000 = 10^^^^^^^^^1000
(2047) myria-dekaxis = E1#1#1#1#1#1#1#1#10,000 = 10^^^^^^^^^10,000
(2048) octadia-dekaxis = E1#1#1#1#1#1#1#1#100,000,000
(2049) sedeniadia-dekaxis = E1#1#1#1#1#1#1#1#10,000,000,000,000,000
...
(2050) deka-dekaxia-dekaxis ✡ = E1#1#1#1#1#1#1#1#10#2
Category 9
Regiment block 11
Members: 63 (47 original + 16 new)
(2051 - 2113)
[9 arrows to 10 arrows]
Why stop at 8? Let's go up to a full 10 regiments before moving on to the next level of sophistication. With that in mind I present the eponymous member of the 9th regiment:
(2051) gargantuul ☆★ = E100#100#100#100#100#100#100#100#100
(short for "gargantuan googol")
Next is ...
(2051) gargantuulennex = E100#100#100#100#100#100#100#100#100#2
(2052) gargantuulduennex = E100#100#100#100#100#100#100#100#100#3
(2053) gargantuultriennex = E100#100#100#100#100#100#100#100#100#4
...
(2054) gargantuulcentiennex = E100#100#100#100#100#100#100#100#100#101
Next we append our suffixes...
(2055) gargantuulding = E500#500#500#500#500#500#500#500#500
...
(2056) gargantuulchime = E1000#1000#1000#1000#1000#1000#1000#1000#1000
(2057) gargantuulennexichime = E1000#1000#1000#1000#1000#1000#1000#1000#1000#2
(2058) gargantuulennexichime = E1000#1000#1000#1000#1000#1000#1000#1000#1000#3
...
(2059) gargantuulbell = E5000#5000#5000#5000#5000#5000#5000#5000#5000#5000
...
(2060) gargantuultoll = E10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000
(2061) gargantuulennexitoll = E10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#2
(2062) gargantuulduennexitoll = E10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#3
Next we can append -gong to these...
(2063) gargantuulgong = E100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000
(2064) gargantuulennexigong = E100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#2
(2065) gargantuulduennexigong = E100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#3
...
(2066) gargantuulbong =
E100,000,000#100,000,000#100,000,000#100,000,000#100,000,000#
100,000,000#100,000,000#100,000,000#100,000,000
(2067) gargantuulennexibong =
E100,000,000#100,000,000#100,000,000#100,000,000#100,000,000#
100,000,000#100,000,000#100,000,000#100,000,000#2
(2068) gargantuulduennexibong =
E100,000,000#100,000,000#100,000,000#100,000,000#100,000,000#
100,000,000#100,000,000#100,000,000#100,000,000#3
...
(2069) gargantuulthrong =
E100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#
100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000
(2070) gargantuulennexithrong =
E100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#
100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#2
(2071) gargantuulduennexithrong =
E100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#
100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#3
...
(2072) gargantuulgandingan =
E100,000,000,000,000#100,000,000,000,000#100,000,000,000,000#100,000,000,000,000#100,000,000,000,000#
100,000,000,000,000#100,000,000,000,000#100,000,000,000,000#100,000,000,000,000
next are the combinatorial googolism's ...
(2073) googolennex = E100#1#1#1#1#1#1#1#1#2
(2074) grangolennex = E100#100#1#1#1#1#1#1#1#2
(2075) greagolennex = E100#100#100#1#1#1#1#1#1#2
(2076) gigangolennex = E100#100#100#100#1#1#1#1#1#2
(2077) gorgegolennex = E100#100#100#100#100#1#1#1#1#2
(2078) gulgolennex = E100#100#100#100#100#100#1#1#1#2
(2079) gaspgolennex = E100#100#100#100#100#100#100#1#1#2
also ...
(2080) gargantuulplex = E(E100#100#100#100#100#100#100#100#100)
(2081) gargantuuldex = E100#(E100#100#100#100#100#100#100#100#100)
(2082) gargantuulthrex = E100#100#(E100#100#100#100#100#100#100#100#100)
(2083) gargantuultetrex = E100#100#100#(E100#100#100#100#100#100#100#100#100)
(2084) gargantuulpentex = E100#100#100#100#(E100#100#100#100#100#100#100#100#100)
(2085) gargantuulhex = E100#100#100#100#100#(E100#100#100#100#100#100#100#100#100)
(2086) gargantuulheptex = E100#100#100#100#100#100#(E100#100#100#100#100#100#100#100#100)
(2087) gargantuuloctex = E100#100#100#100#100#100#100#(E100#100#100#100#100#100#100#100#100)
= E100#100#100#100#100#100#100#100#101
Next the in-betweens ...
between a gargantuul and a gargantuulennex ...
(2088) ginorgolennex = E100#100#100#100#100#100#100#100#1#2
(2089) ginorgoloctexiennex = E100#100#100#100#100#100#100#100#2#2
(2090) ginorgolduoctexiennex = E100#100#100#100#100#100#100#100#3#2
between a gargantuulennex and a gargantuulduennex ...
(2091) ginorgolduennex = E100#100#100#100#100#100#100#100#1#3
(2092) ginorgoloctexiduennex = E100#100#100#100#100#100#100#100#2#3
(2093) ginorgolduoctexiduennex = E100#100#100#100#100#100#100#100#3#3
...
We can also apply the new suffix -ennex to eceton...
(2094) ecetonennex = E303#1#1#1#1#1#1#1#1#2
(2095) ecetonduennex = E303#1#1#1#1#1#1#1#1#3
With eceto- prefix...
(2096) eceto-gargantuul = E303#303#303#303#303#303#303#303#303
(2097) eceto-gargantuulennex = E303#303#303#303#303#303#303#303#303#2
(2098) eceto-gargantuulduennex = E303#303#303#303#303#303#303#303#303#3
Lastly we have the endekaxis series...
(2099) tria-endekaxis ⍟ = E1#1#1#1#1#1#1#1#1#3 = 10^^^^^^^^^^3
(2100) tetra-endekaxis ⍟ = E1#1#1#1#1#1#1#1#1#4 = 10^^^^^^^^^^4
(2101) penta-endekaxis = E1#1#1#1#1#1#1#1#1#5 = 10^^^^^^^^^^5
(2102) hexa-endekaxis = E1#1#1#1#1#1#1#1#1#6 = 10^^^^^^^^^^6
(2103) hepta-endekaxis = E1#1#1#1#1#1#1#1#1#7 = 10^^^^^^^^^^7
(2104) octa-endekaxis = E1#1#1#1#1#1#1#1#1#8 = 10^^^^^^^^^^8
(2105) enna-endekaxis = E1#1#1#1#1#1#1#1#1#9 = 10^^^^^^^^^^9
(2106) deka-endekaxis ⍟☆★ = E1#1#1#1#1#1#1#1#1#10 = 10^^^^^^^^^^10
(A deka-endekaxis is equivalent to a tridecal in Bowers' system)
...
(2107) icosa-endekaxis = E1#1#1#1#1#1#1#1#1#20 = 10^^^^^^^^^^20
(2108) hecta-endekaxis ⍟☆ = E1#1#1#1#1#1#1#1#1#100 = 10^^^^^^^^^^100
(2109) chilia-endekaxis = E1#1#1#1#1#1#1#1#1#1000 = 10^^^^^^^^^^1000
(2110) myria-endekaxis = E1#1#1#1#1#1#1#1#1#10,000 = 10^^^^^^^^^^10,000
(2111) octadia-endekaxis = E1#1#1#1#1#1#1#1#1#100,000,000
(2112) sedeniadia-endekaxis = E1#1#1#1#1#1#1#1#1#10,000,000,000,000,000
...
(2113) deka-endekaxia-endekaxis ✡ = E1#1#1#1#1#1#1#1#1#10#2
Category 10
Regiment block 12
Members: 183 (77 original + 106 new)
(2114 - 2296)
[10 arrows to the limit of the up-arrow notation]
Level 1 | Stage 2-5
Stage 2-5 ~ Now we reach the tenth series of the Hyper-E notation in which will pass the limit of the primitive recursive function level.
At last we reach the Googondol Regiment, the 10th Regiment. It includes:
(2114) googondol ☆★ = E100#100#100#100#100#100#100#100#100#100
(short for "googondo googol")
(2115) googondoldecex = E100#100#100#100#100#100#100#100#100#100#2
(2116) googondoldudecex = E100#100#100#100#100#100#100#100#100#100#3
(2117) googondoltridecex = E100#100#100#100#100#100#100#100#100#100#4
...
(2118) googondolcentidecex = E100#100#100#100#100#100#100#100#100#100#101
now we can apply our suffixes ...
(2119) googondolding = E500#500#500#500#500#500#500#500#500#500
...
(2120) googondolchime = E1000#1000#1000#1000#1000#1000#1000#1000#1000#1000
(2121) googondoldecexichime = E1000#1000#1000#1000#1000#1000#1000#1000#1000#1000#2
(2122) googondoldudecexichime = E1000#1000#1000#1000#1000#1000#1000#1000#1000#1000#3
...
(2123) googondolbell = E5000#5000#5000#5000#5000#5000#5000#5000#5000#5000
...
(2124) googondoltoll = E10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000
(2125) googondoldecexitoll = E10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#2
(2126) googondoldudecexitoll = E10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#3
...
(2127) googondolgong
= E100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000
(2128) googondoldecexigong
= E100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#2
(2129) googondoldudecexigong
= E100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#3
...
(2130) googondolbong
= E100,000,000#100,000,000#100,000,000#100,000,000#100,000,000#
100,000,000#100,000,000#100,000,000#100,000,000#100,000,000
(2131) googondoldecexibong
= E100,000,000#100,000,000#100,000,000#100,000,000#100,000,000#
100,000,000#100,000,000#100,000,000#100,000,000#100,000,000#2
(2132) googondoldudecexibong
= E100,000,000#100,000,000#100,000,000#100,000,000#100,000,000#
100,000,000#100,000,000#100,000,000#100,000,000#100,000,000#3
...
(2133) googondolthrong
= E100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#
100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000
(2134) googondoldecexithrong
= E100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#
100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#2
(2135) googondoldudecexithrong
= E100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#
100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#100,000,000,000#3
...
(2136) googondolgandingan
= E100,000,000,000,000#100,000,000,000,000#100,000,000,000,000#100,000,000,000,000#100,000,000,000,000#
100,000,000,000,000#100,000,000,000,000#100,000,000,000,000#100,000,000,000,000#100,000,000,000,000
next are the combinatorial googolism's ...
(2137) googoldecex = E100#1#1#1#1#1#1#1#1#1#2
(2138) grangoldecex = E100#100#1#1#1#1#1#1#1#1#2
(2139) greagoldecex = E100#100#100#1#1#1#1#1#1#1#2
(2140) gigangoldecex = E100#100#100#100#1#1#1#1#1#1#2
(2141) gorgegoldecex = E100#100#100#100#100#1#1#1#1#1#2
(2142) gulgoldecex = E100#100#100#100#100#100#1#1#1#1#2
(2143) gaspgoldecex = E100#100#100#100#100#100#100#1#1#1#2
(2144) ginorgoldecex = E100#100#100#100#100#100#100#100#1#1#2
also ...
(2145) googondolplex = E(E100#100#100#100#100#100#100#100#100#100)
(2146) googondoldex = E100#(E100#100#100#100#100#100#100#100#100#100)
(2147) googondolthrex = E100#100#(E100#100#100#100#100#100#100#100#100#100)
(2148) googondoltetrex = E100#100#100#(E100#100#100#100#100#100#100#100#100#100)
(2149) googondolpentex = E100#100#100#100#(E100#100#100#100#100#100#100#100#100#100)
(2150) googondolhex = E100#100#100#100#100#(E100#100#100#100#100#100#100#100#100#100)
(2151) googondolheptex = E100#100#100#100#100#100#(E100#100#100#100#100#100#100#100#100#100)
(2152) googondoloctex = E100#100#100#100#100#100#100#(E100#100#100#100#100#100#100#100#100#100)
(2153) googondolennex = E100#100#100#100#100#100#100#100#(E100#100#100#100#100#100#100#100#100#100)
= E100#100#100#100#100#100#100#100#100#101
...
next the in-betweens ...
in between googondol and googondoldecex are ...
(2154) gargantuuldecex = E100#100#100#100#100#100#100#100#100#1#2
(2155) gargantuulennexidecex = E100#100#100#100#100#100#100#100#100#2#2
(2156) gargantuulduennexidecex = E100#100#100#100#100#100#100#100#100#3#2
...
in between googondoldecex and googondoldudecex are ...
(2157) gargantuuldudecex = E100#100#100#100#100#100#100#100#100#1#3
(2158) gargantuulennexidudecex = E100#100#100#100#100#100#100#100#100#2#3
(2159) gargantuulduennexidudecex = E100#100#100#100#100#100#100#100#100#3#3
...
applying -decex to eceton- we get...
(2160) ecetondecex = E303#1#1#1#1#1#1#1#1#1#2
(2161) ecetondudecex = E303#1#1#1#1#1#1#1#1#1#3
etc.
applying eceto- to googondol we get...
(2162) eceto-googondol = E303#303#303#303#303#303#303#303#303#303
(2163) eceto-googondoldecex = E303#303#303#303#303#303#303#303#303#303#2
(2164) eceto-googondoldudecex = E303#303#303#303#303#303#303#303#303#303#3
Lastly we have the -dodekaxis series (with eleven arrows) ...
(2165) tria-dodekaxis ⍟ = E1#1#1#1#1#1#1#1#1#1#3 = 10^^^^^^^^^^^3
(2166) tetra-dodekaxis ⍟ = E1#1#1#1#1#1#1#1#1#1#4 = 10^^^^^^^^^^^4
(2167) penta-dodekaxis = E1#1#1#1#1#1#1#1#1#1#5 = 10^^^^^^^^^^^5
(2168) hexa-dodekaxis = E1#1#1#1#1#1#1#1#1#1#6 = 10^^^^^^^^^^^6
(2169) hepta-dodekaxis = E1#1#1#1#1#1#1#1#1#1#7 = 10^^^^^^^^^^^7
(2170) octa-dodekaxis = E1#1#1#1#1#1#1#1#1#1#8 = 10^^^^^^^^^^^8
(2171) enna-dodekaxis = E1#1#1#1#1#1#1#1#1#1#9 = 10^^^^^^^^^^^9
(2172) deka-dodekaxis ⍟☆ = E1#1#1#1#1#1#1#1#1#1#10 = 10^^^^^^^^^^^10
...
(2173) icosa-dodekaxis = E1#1#1#1#1#1#1#1#1#1#20 = 10^^^^^^^^^^^20
(2174) hecta-dodekaxis ⍟☆ = E1#1#1#1#1#1#1#1#1#1#100 = 10^^^^^^^^^^^100
(2175) chilia-dodekaxis = E1#1#1#1#1#1#1#1#1#1#1000 = 10^^^^^^^^^^^1000
(2176) myria-dodekaxis = E1#1#1#1#1#1#1#1#1#1#10,000 = 10^^^^^^^^^^^10,000
(2177) octadia-dodekaxis = E1#1#1#1#1#1#1#1#1#1#100,000,000
(2178) sedeniadia-dodekaxis = E1#1#1#1#1#1#1#1#1#1#10,000,000,000,000,000
...
(2179) deka-dodekaxia-dodekaxis = E1#1#1#1#1#1#1#1#1#1#10#2
Notice how these expressions are getting pretty long? We can shorten them. Let...
Ea##b = Ea#a#a# ... #a#a#a w/ b a's
Thus we have ...
googondol = E100##10
As the sequence:
googol = E100##1 = E100
grangol = E100##2 = E100#100
greagol = E100##3 = E100#100#100
gigangol = E100##4 = E100#100#100#100
...
This suggests even larger numbers! We can form these by combining the power of the "##", or deutero-hyperion, with the power of the "#" , or proto-hyperion.
First, we define E100##11 as:
(2180) googoadol ☆ = E100##11 = E100#100#100#100#100#100#100#100#100#100#100
But why I am not done with googoadol yet. I need to define some extensions to "googoadol" with -endecex, power modifiers, and -triadekaxis to finish this.
(2181) googoadolendecex = E100#100#100#100#100#100#100#100#100#100#100#2
(2182) googoadolduendecex = E100#100#100#100#100#100#100#100#100#100#100#3
etc.
(2183) googoadolchime = E1000##11 = E1000#1000#1000#1000#1000#1000#1000#1000#1000#1000#1000
(2184) googoadoltoll = E10,000##11
= E10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000#10,000
(2185) googoadolgong = E100,000##12
= E100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000#100,000
etc.
(2186) ecetonendecex = E303#1#1#1#1#1#1#1#1#1#1#2
(2187) eceto-googoadol = E303##11 = E303#303#303#303#303#303#303#303#303#303#303
etc.
(2188) tria-triadekaxis = E1#1#1#1#1#1#1#1#1#1#1#3 (12 arguments)
= 10^^^^^^^^^^^^3 (12 arrows) = 10{12}3
(2189) tetra-triadekaxis = E1#1#1#1#1#1#1#1#1#1#1#4 (12 arguments)
= 10^^^^^^^^^^^^4 (12 arrows) = 10{12}4
(2190) deka-triadekaxis = E1#1#1#1#1#1#1#1#1#1#1#10 (12 arguments)
= 10^^^^^^^^^^^^10 (12 arrows) = 10{12}10
(2191) hecta-triadekaxis = E1#1#1#1#1#1#1#1#1#1#1#100 (12 arguments)
= 10^^^^^^^^^^^^100 (12 arrows) = 10{12}100
etc.
... moving on...
(2192) goograndol ☆ = E100##12 = E100#100#100#100#100#100#100#100#100#100#100#100
with extensions of goograndol...
(2193) goograndoldodecex = E100#100#100#100#100#100#100#100#100#100#100#100#2
This can also be simplified to...
E(100##12)#2
(This is not to be confused with E100##12#2 in Extended Hyper-E notation.)
(2194) goograndol-dudodecex = E(100##12)#3
...
(2195) goograndolchime = E1000##12
(2196) goograndoltoll = E10,000##12
(2197) goograndolgong = E100,000##12
...
(2198) tria-tetradekaxis = E1#1#1#1#1#1#1#1#1#1#1#1#3 (13 arguments)
= 10^^^^^^^^^^^^^3 = 10{13}3
(2199) tetra-tetradekaxis = E1#1#1#1#1#1#1#1#1#1#1#1#4 (13 arguments)
= 10^^^^^^^^^^^^^4 = 10{13}4
(2200) deka-tetradekaxis = E1#1#1#1#1#1#1#1#1#1#1#1#10 (13 arguments)
= 10^^^^^^^^^^^^^10 = 10{13}10
(2201) tria-tetradekaxis = E1#1#1#1#1#1#1#1#1#1#1#1#100 (13 arguments)
= 10^^^^^^^^^^^^^100 = 10{13}100
...
then...
(2202) googreadol = E100##13 = E100#100#100#100#100#100#100#100#100#100#100#100#100
(2203) googreagoltriadecex = E(100##13)#2
(2204) googreadolgong = E100,000##13
...
(2205) tria-pentadekaxis = E1#1#1#1#1#1#1#1#1#1#1#1#1#3 (14 arguments)
= 10^^^^^^^^^^^^^^3 = 10{14}3
(2206) tetra-pentadekaxis = E1#1#1#1#1#1#1#1#1#1#1#1#1#4 (14 arguments)
= 10^^^^^^^^^^^^^^4 = 10{14}4
(2207) deka-pentadekaxis = E1#1#1#1#1#1#1#1#1#1#1#1#1#10 (14 arguments)
= 10^^^^^^^^^^^^^^10 = 10{14}10
(2208) hecta-pentadekaxis = E1#1#1#1#1#1#1#1#1#1#1#1#1#100 (14 arguments)
= 10^^^^^^^^^^^^^^10 = 10{14}100
...
(2209) googigandol = E100##14 = E100#100#100#100#100#100#100#100#100#100#100#100#100
(2210) googigandoltetradecex = E(100##14)#2
(2211) googigandolgong = E100,000##14
...
(2212) googorgedol = E100##15 = E100#100#100#100#100#100#100#100#100#100#100#100#100#100
(2213) googuldol = E100##16
(2214) googaspdol = E100##17
(2215) googinordol = E100##18
(2216) googarganduul = E100##19
(2217) googonkosol ☆ = E100##20
This expands:
E100#100#100#100#100#100#100#100#100#100#100#100#100#100#100#100#100#100#100#100
I am not done with this combination yet. To continue further:
For nth Hyper-E naming system: (goo-n-ol) (corresponds to E100##n)
(for 1-9 naming, ignore the goo prefix) But, if it has a gargan, replace "-ol" with "-uul"
(note that 10 naming (googondol) is not actually based on the naming system above)
... from 21 to 29...
(2218) googoakosol = E100##21
(2219) googrankosol = E100##22
(2220) googreakosol = E100##23
(2221) googigankosol = E100##24
(2222) googorgekosol = E100##25
(2223) googulkosol = E100##26
(2224) googaspkosol = E100##27
(2225) googinorkosol = E100##28
(2226) googargankosuul = E100##29
... from 30 to 39...
(2227) googontritol = E100##30
(2228) googoatritol = E100##31
(2229) goograntritol = E100##32
(2230) googreatritol = E100##33
(2231) googigantritol = E100##34
(2232) googorgetritol = E100##35
(2233) googultritol = E100##36
(2234) googasptritol = E100##37
(2235) googinortritol = E100##38
(2236) googargantrituul = E100##39
... and more ...
(2237) googonsartol = E100##40
(2238) googransartol = E100##42
(2239) googorgesartol = E100##45
(2240) googonpetol = E100##50
(2241) googorgepetol = E100##55
(2242) googonextol = E100##60
(2243) googorgeextol = E100##65
... the nice one ...
(2244) googarganextuul = E100##69
...
(2245) googoneptol = E100##70
(2246) googorgeeptol = E100##75
(2247) googonogdol = E100##80
(2248) googorgeogdol = E100##85
(2249) googonentol = E100##90
(2250) googorgeentol = E100##95
(2251) googarganentuul = E100##99
...
(2252) googonhectol ☆ = E100##100
We can also continue further beyond 100, using "hundreds" roots as follows:
(2253) googoahectol = E100##101
(2254) googranhectol = E100##102
(2255) googreahectol = E100##103
(2256) googiganhectol = E100##104
(2257) googorgehectol = E100##105
How about E100##110? Guess what, the naming gaps were already filled. I was going googondo for generalized naming system beyond googondol whatsoever. But, one ubiquitous issue. Using the root: -do- + -hectol (meaning 110), and -dohectol (meaning 200), it would result in the same names. They are splitted into two identical "googondohectol"s
I eradicate -do- into -da- for 10s plus hundreds in E100##n. In that case, just replace "o" with "a" from "-do-" into "-da-".
(2258) googondahectol = E100##110
(2259) googoadahectol = E100##111
(2260) goograndahectol = E100##112
... moving on 120th ...
(2261) googonkoshectol = E100##120
(2262) googontrithectol = E100##130
(2263) googonsarthectol = E100##140
(2264) googonpethectol = E100##150
...
We also have 200th, 300th, 400th members as follows...
(2265) googondohectol = E100##200
(2266) googontriahectol = E100##300
(2267) googontetrahectol = E100##400
(2268) googonpentahectol = E100##500
(2269) googonhexahectol = E100##600
(2270) googonheptahectol = E100##700
(2271) googonoctahectol = E100##800
(2272) googonennahectol = E100##900
...
(2273) googonentennahectol = E100##990
(2274) googarganentennahectuul = E100##999
...
(2275) googonchilol = E100##1000
*formerly googonchiliol
We can continue even further with...
(2276) googonmyriol = E100##10,000
(2277) googonhecta-chilol = E100##100,000
*formerly googonhecta-chiliol
(2278) googonchilia-chilol = E100##1,000,000
*formerly googonchilia-chiliol
(2279) googonchilia-myriol = E100##10,000,000
(2280) googonmyria-myriol = E100##100,000,000
(also called (2281) googonoctadol)
(2282) googonsedeniadol = E100##10,000,000,000,000
To go even further I introduce the great operator. It allows for diagonalization on the next level. We have...
(2283) great googol ☆ = E100##1#2 = E100##(E100##1#1) = E100##(E100) = E100##(10^100) = E100##(googol)
= E100#100#100#100# ... ... ... ... ... ... ... ... #100#100#100#100 (w/ 10^100 100's)
o_0;
With that in mind we can go much further ...
(2284) great grangol ☆ = E100##2#2 = E100##(E100#100)
(2285) great greagol = E100##3#2 = E100##(E100#100#100)
(2286) great gigangol = E100##4#2 = E100##(E100#100#100#100)
(2287) great gorgegol = E100##5#2 = E100##(E100#100#100#100#100)
(2288) great gulgol = E100##6#2 = E100##(E100#100#100#100#100#100)
(2289) great gaspgol = E100##7#2 = E100##(E100#100#100#100#100#100#100)
(2290) great ginorgol = E100##8#2 = E100##(E100#100#100#100#100#100#100#100)
(2291) great gargantuul = E100##9#2 = E100##(E100#100#100#100#100#100#100#100#100)
and finally ...
(2292) great googondol = E100##10#2
= E100##(E100#100#100#100#100#100#100#100#100#100) = E100##(E100##10) = E100##(googondol)
= E100#100#100#100#100# ... ... ... ... ... ... ... ... ... ... #100#100#100#100#100 (w/ googondol 100s)
o_0;;;
THAT's where we are headed next!
and even more...
(2293) great googonkosol = E100##20#2 = E100##(E100##20)
(2294) great googonhectol ☆ = E100##100#2 = E100##(E100##100)
(2295) great googonchilol = E100##1000#2
*formerly great googonchiliol
(2296) great googonmyriol ✡ = E100##10,000#2
We've exhausted the limits of the basic Hyper-E notation (E#)! Now we begin the extended Hyper-E notation (xE#)!
And at this point, we are not in a half way, fourth way, tenth way, or even a twentieth way done, since there are more than 50,000 "(2) dust mite" googolisms and more than 100 parts in the whole series.