Vast Irregulars of Goals

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Vast Irregulars of Goals is a series of 150 numbers defined by googology user ARsygo.^[1] Note that the 137th number in the series based off Oblivion is ill-defined.

List of numbers[]

#	Name	Value	FGH approximation ^{[note 1]}
1	Done gong	E[15]654,000#56 in Hyper-E notation	\(f_2^{56}(769163)\)
2	Creasing wights	E100#3#(5E100)#3#4 in Hyper-E notation	\(f_5^4(f_4^3(f_3(f_2(324))))\)
3	Orca trek kit	E[56]10###10###10##80##2 in Extended Hyper-E notation	\(f_{\omega^2 2 + \omega+1}(80)\)
4	Leudaren flashes	{3,9,1,1,3,3,3} in BEAF	\(f_{\omega^4 2 + \omega^3 2 + \omega^2 2}(9)\)
5	Maarnee of woks	1.0715*10^111,111	\(f_2(369084)\)
6	Wreak oaf meson	{{12,12,12},8,8,8,8} in BEAF	\(f_{\omega^2 7 + \omega 7 + 7}(8)\)
7	Beggard antre khi	(0)(1)(2)(3)(1)(2)[15] in Bashicu matrix system with respect to version 4 (simulating Hardy hierarchy)	\(f_{\omega^{\omega}+\omega}(15)\) (exact)
8	Fact we fogy kith	105^{(2*10^10)⁶⁰⁰³} ~ 10^{10⁶¹⁸³⁸}	\(f_2^2(205400)\)
9	Actkeg whiff ty	{8,8,8,16,1,1,8} in BEAF	\(f_{\omega^4 7+ \omega 16 + 8}(8)\)
10	Grim unshorn	{3,3^3^3,1,19(3)3} in BEAF	\(f_{\omega^{\omega^3}2+\omega+18}(3^{3^3})\)
11	Stuff icecream foil	{10,10,10,1,1,1,11(10(5)10)2} in BEAF	\(f_{\omega^{\omega^{\omega^{\omega^5}9+9}}+\omega^5 11+\omega+10}(10)\)
12	Facto me fur felicis	{10,10,2,7625597484987,2[googol+1\7625597484985]1,2} in Bird's array notation	\(f_{\varepsilon_\omega}(3^{27})\)
13	Electra sic fifi fumo	{10,10,{10,10,7625597484985},1,2} in BEAF	\(f_{\omega^2 + \omega}(f_{\omega}(7625597484984))\)
14	Forty maser	M(40,maser) = M(40,256) in Hyper-Moser notation	\(f_{258}(40)\)
15	Double forty maser	M(40,40,256) in Hyper-Moser notation	\(f_{\omega256+40}(40)=f_{\omega257}(40)\)
16	One mow my	\(g_{\Gamma_0}(10)\) in slow-growing hierarchy	\(f_{\omega+1}(10)\)
17	Kilts en vos	E100######100###100##8 in Extended Hyper-E notation	\(f_{\omega^5 + \omega^2 + 7}(100)\)
18	Sein volk st	{10,10,1,19(3,3)3} in BEAF	\(f_{\omega^{\omega^{\omega \times 2 + 3}}\times 2 + \omega 18}(10)\)
19	Shellac clot	3↑^{(G(15)^G(15))} 3 (where G(15) is the 15th sequence of Graham's function)	\(f_{\omega+1}(16)\)
20	Chal collets	(0,0,0)(1,1,1)(1,1,0) [400] in Bashicu matrix system with respect to version 4 (simulating Hardy hierarchy)	\(f_{\psi_0(\Omega_\omega+\Omega)}(400)\)
21	La slecht col	E100#^(#^###^###^##)7 in Cascading-E notation	\(f_{\omega^{\omega^{\omega^2}\times 3}[7]}(100)\)
22	Dandy strani velde	1.3407*10⁶⁵⁸	\(f_2(2175)\)
23	Baga engendra	45[67] in Copy notation	\(f_2(435)\)
24	Garage baga engendra	23[45[67]] in Copy notation	\(f_2^2(434)\)
25	Bane gad range	M₉₆₇ (Mersenne number, 2⁹⁶⁷-1)	\(f_2(957)\)
26	Bang and eager	M₈₀₀₉ (Mersenne number, 2⁸⁰⁰⁹-1)	\(f_2(7996)\)
27	Lick hauchten typisiert ste	{53,13[3\2\6,6]4} in Bird's array notation	\(f_{(\varepsilon_{\zeta_{\omega4+5}+1})^{\omega^2}}(13)\)
28	Unaq va unaq	(44↑↑3)↑↑↑5	\(f_4(5)\)
29	Wftrt gpyopeel	(0)(1)(2)(3)(4)(5)(6)(7)[96420] in Bashicu matrix system with respect to version 4 (simulating Hardy hierarchy)	\(f_{\omega↑↑6}(96420)\) (exact)
30	A doze pol	10^1,503	\(f_2(4979)\)
31	N qbmr cby	A doze pol^1,503 = 10^2,259,009	\(f_2(7\,504\,242)\)
32	Wain veiled	E(garpo)#42096#96420 = E7744#42096#96420 Hyper-E notation	\(f_3(96420)\)
33	Jnva irvyrq	(smallest 1001-digit prime)² = (10¹⁰⁰⁰ + 453)²	\(f_2(6631)\)
34	A manacled older resorts	{34,gartreys,1,2,3,4} = {34,1089,1,2,3,4} in BEAF	\(f_{\omega^3 3+\omega^2 3+\omega2}(1089)\)
35	J vjwjlunm xumna anbxacb	{62, 53, 4, 35, 26} in BEAF	\(f_{\omega^2 25+\omega35+4}(53)\)
36	Fee gunther	12345!	\(f_2(149969)\)
37	Fuehrer gent	A(6,7,4) in multivariable Ackermann notation	\(f_{\omega6+7}(4)\)
38	Prefer ten ugh	10^M₅₂₁ = 10^2⁵²¹-1 (M₅₂₁ is a Mersenne prime)	\(f_2(M_{521}) \approx f_2^2(512)\)
39	Rheg free gunther	447^{4^4⁷} = 447^{2^32,768}	\(f_2^2(32768)\)
40	Trash talk	{720,120,24,6,4} in BEAF	\(f_{\omega^2 3+\omega6+24}(120)\)
41	Talk talkh	E42096#40585#96420 in Hyper-E notation	\(f_3(96420)\)
42	Poll Position	A(5,5,5,5,6) in multivariable Ackermann notation	\(f_{\omega^3 5+\omega^2 5 +\omega5+5}(6)\)
43	Poll Position on Talk	A(5,5,5,5,6,7) in multivariable Ackermann notation	\(f_{\omega^4 5+\omega^3 5 +\omega^2 5+\omega5+6}(7)\)
44	Held enough rot	A(5,5,5,5,6,7,7,7) in multivariable Ackermann notation	\(f_{\omega^6 5 + \omega^5 5 +\omega^4 5+\omega^3 5+\omega^2 6+\omega7+7}(7)\)
45	Brace waned pan crew	5[6][7] in Steinhaus-Moser notation	\(f_5(f_4(5))\)
46	Baa manners	{10,679,702,112} in BEAF	\(f_{\omega111+702}(679)\)
47	Baa mandrel bents bends	Concatenation of 5[555] and 7[777] in copy notation = 5555....5557777.....7777 = \(\lfloor 5/9\times10^{555}\rfloor\times10^{777}+\lfloor 7/9\times10^{777}\rfloor\)	\(f_2(4411)\)
48	Bee Awesome	3,094,320,024,810,980,923,801,401	\(f_2(75)\)
49	Mesa bee woe	Onion! = 21,042,141,113,214,300!	\(f_2^2(52)\)
50	Nerves of Steal	Ozone^Faxul	\(f_2^2(1236)\)
51	Eleven Frosts	(0)(1)(2)(3)(4)(3)(4)[11] in BMS with respect to v4 (simulating Hardy hierarchy)	\(f_{\omega^{\omega^{\omega2}}}(11)\) (exact)
52	Eleven Front Softeners	1331!1 in hyperfactorial array notation	\(f_3(1327)\)
53	Big Mouth	E20###^^^###>#^^#(guppy) = E20###^^^###>#^^#(E20) in Extended Cascading-E notation	\(f_{\varphi(1,2,\varepsilon_0)}(f_2(61))\)
54	Big Hot Mouth	E20###^^^#^#>#^^#(big mouth) = E20###^^^#^#>#^^#(E20###^^^###>#^^#(E20)) in Extended Cascading-E notation	\(f_{\varphi(1,2,\varepsilon_0)}^2(f_2(61))\)
55	BBQ Big Mouth	E20###^^^#^^###100 in Extended Cascading-E notation	\(f_{\varphi(1,\eta_0,0)}(100)\)
56	Cays tool	s(10,1500{1,,1,2,,2}2) in strong array notation	\(f_{\psi_\Omega(\chi_0(\chi_1(0)+\omega))(0)}(1500)\)
57	Talc so to	\(H_{\omega^{\omega^5}}(100)\) in Hardy hierarchy	\(f_{\omega^5}(100)\) (exact)
58	Teased math juice	420! + 96!	\(f_2(3048)\)
59	Teased orange juice	450! * 300!	\(f_2(5352)\)
60	Locked Out	2020↑2021↑↑2022	\(f_3(2022)\)
61	Lucked Too	2022↑↑755	\(f_3(755)\)
62	Coke d Lout	{10,10,tetratri,1,2} = {10,10,{3,3,3,3},1,2} in BEAF	\(f_{\omega^2+\omega}(f_{\omega^2}(3))\)
63	Say Cheese	Curry ↓↓ 15 = 4,194,304 ↓↓ 15 in Down-arrow notation	\(f_3(15)\)
64	Stay Parmesan Cheese	{12,14[15,16]18} in BAN	\(f_{\omega^{\omega^{\omega15+14}}17}(14)\)
65	Googolcrumbs to chunks	googolchunk * googolcrumb = 10⁹⁹ * 10⁹⁵ = 10¹⁹⁴	\(f_2(625)\)
66	A flan against dints	42470!2 in hyperfactorial array notation	\(f_4(42470)\)
67	Gym Dandy	384³⁸⁴²	\(f_2(32968)\)
68	Shatter jug	83726037! ~ 6.61604 × 10^626987962	\(f_2^2(24)\)
69	SMN' apprehendere	googol in a giggol-gon = 10¹⁰⁰[10↑↑100] in Steinhaus Moser notation	\(f_{\omega}(f_3(324))\)
70	Abstrused E	E2514###^^#^#^###78#^#37##39 in Extended Cascading-E notation	\(f_{\varphi(\omega^{\omega^3},0)+\omega^\omega+\omega}(39)\)
71	Abstrused nested array (BEAF)	{24,252(10,10(23,78(45)4)34)25} in BEAF	\(f_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega}4+\omega78+23}34+\omega10+10}}}25}(10)\)
72	Chicken chasseur	{3,6,1,1,1,1,4,9} in BAN	\(f_{\omega^5 8+\omega^4 3}(6)\)
73	Bevellers of gong	100000![4,2] in hyperfactorial array notation	\(f_{\omega2+3}(100000)\)
74	Suboptimal multidimensional apprehendere	{17,17 [4] 1 [4] 1 [2] 1 [2] 1 [2] 2} in Bird's array notation	\(f_{\omega^{\omega^4 2+\omega2}}(17)\)
75	Agitato cuatro	{16,16 [2,2]1[2]2} in BAN	\(f_{\omega^{\omega^{\omega+1}+\omega2}}(16)\)
76	Inexact beauty	E42096##96	\(f_{97}(42096)\)
77	G-force brick wall	{256,3,3,4,5,6,7,8,9,200} in BEAF	\(f_{\omega^7 199 +\omega^6 8+\omega^5 7+\omega^4 6 +\omega^3 5+\omega^2 4+\omega3+2}(3)\)
78	Second G-force brick wall	{400,500,600,700,900,10,20,30,40} in BEAF	\(f_{\omega^6 39+\omega^5 29+\omega^4 19+\omega^3 9+\omega^2 899+\omega699+599}(500)\)
79	Oversupinated array	{69720,15(96,96,1,1)2} in BEAF	\(f_{\omega^{\omega^{\omega^3 +\omega^2 +\omega96+96}}}(15)\)
80	Strong apprehendere	s(10,11,3,1,1,1,1,1,4,4) in SAN	\(f_{\omega^7 3+\omega^6 3+2}(11)\)
81	Clash of the prime Titans	(10⁹⁹⁹+7)^{(10⁹⁹⁹+663)}	\(f_2(3295)\)
82	Clash of the tetrated prime Titans	(10⁹⁹⁹+7)↑↑(10⁹⁹⁹+663)	\(f_3(f_2(3295))\)
83	Bienvenido al Desfile Negro	{3,6,2,3,6,3,6,3,3,9} in BEAF	\(f_{\omega^7 8+\omega^6 2+\omega^5 2+\omega^4 5+\omega^3 2+\omega^2 5+\omega2+1}(6)\)
84	Willkommen bei der schwarzen Parade	{4,3,1,1,5,3,2,6} in BEAF	\(f_{\omega^5 5+\omega^4 1+\omega^3 2+\omega^2 4}(3)\)
85	Schwarzen Parade apprehendere	E100#^#Willkommen bei der schwarzen Parade ~ E100#^#(E10#^#8)	\(f_{\omega^{\omega}}(f_{\omega^5 5+\omega^4 1+\omega^3 2+\omega^2 4}(3))\)
86	Interlude	{Gym Dandy, Say Cheese, Rheg free gunther, Mesa bee woe} in BEAF	\(f_{\omega^2}(f_2^2(52))\)
87	Qbhpur ont	10↑↑↑juice↑↑fznine	\(f_4(f_3(f_2(24)))\)
88	Grand qbhpur ont	100↑↑↑↑qbhpur ont	\(f_5(f_4(f_3(f_2(24))))\)
89	Great qbhpur ont	{10,10,qbhpur ont} in BEAF	\(f_{\omega}(f_4(f_3(f_2(24))))\)
90	Dual-great qbhpur ont	s(10,10,10,qbhpur ont) in SAN	\(f_{\omega^2}(f_4(f_3(f_2(24))))\)
91	Cascading juggernaut	E[25]Borges' number#^(#^#^#^#^##^#^##^#)3898 in Cascading-E notation	\(f_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega}}}+\omega^{\omega}+\omega}}}(3898)\)
92	Extended cascading juggernaut	E500#^^^^^^^^^^########^^^^^^^^^#^^^^^^^#>#^^^#^^#100 in Extended Cascading-E notation	\(f_{\varphi(8,\varphi(7,\varphi(5,0,0),0)+7,\varphi(1,0,\varepsilon_0))}(100)\)
93	Pinto bean	3⁶⁷	\(f_2(99)\)
94	Dual pinto beans	3↑↑67	\(f_3(67)\)
95	Far and away	Pinto bean!2 in Hyperfactorial array notation	\(f_4(f_2(67))\)
96	A Strong Beautiful Array Mind (abbreviated as A.S.B.A.M)	s(3,far and away,4,5,6,7) in SAN	\(f_{\omega^3 6+\omega^2 5+\omega5+4}(f_4(f_2(67))\)
97	A beautiful BA array mind	{3,A.S.B.A.M[4,5,6]7} in Bird's array notation	\(f_{\omega^{\omega^{\omega^2 5+\omega4+3}}7}(f_{\omega^3 6+\omega^2 5+\omega5+4}(f_4(f_2(67)))\)
98	Multivariated masurium	A(43,43,1,0,0,0,0,0,2) in Taro's multivariable Ackermann notation	\(f_{\omega^7 43+\omega^6 43+\omega^5}(2)\)
99	Isolated masurium	A(99,99,43,1,0,0,0,0,0,3) in Taro's multivariable Ackermann notation	\(f_{\omega^8 99+\omega^7 99+\omega^6 43+\omega^5}(3)\)
100	Alpha decayed letters	3A3 in Greek Letter Notation	\(f_{\omega^2}^3(3)\)
101	supinated betas	5B2 in Greek Letter Notation	\(f_{\omega^2 2}^2(5)\)
102	The Powering Wilter / The powering wilter	(0)(1)(0)(1)[16] in BMS v4 (simulating Hardy hierarchy)	\(f_1(f_1(16))\) (exact)
103	Ninety Goth / ninety goth	(0)(1)(1)[90] in BMS v4 (simulating Hardy hierarchy)	\(f_2(90)\) (exact)
104	Nongenti Oh Tiny	900²⁷⁰³	\(f_2(26497)\)
105	Nine Got Thy / nine got thy	(0)(1)(2)(2)(1)(2)[9] in BMS v4	\(f_{\omega^{\omega^2 +\omega}}(9)\)
106	Ten trying, oh	(0)(1)(2)(2)(2)[10] in BMS v4	\(f_{\omega^{\omega^3}}(9)\)
107	Ten trying gammas	4G5 in Greek Letter Notation	\(f_{\omega^2 3}^5(4)\)
108	Hoofed it	(15{3,5}16) in Notation Array Notation	\(f_{\omega14}(15)\)
109	Yadda yadda hoofed!	24!4 in Hyperfactorial Array notation	\(f_6(24)\)
110	Fizzy pickle	E96#^#^#Never gonna give you up in Cascading-E notation	\(f_{\omega^{\omega^{\omega}}}(f_{\omega^{\omega2}}(69))\)
111	Alight is out	{10,ascendhex,5,6,7,8} = {10,{2,3,4,5,6},5,6,7,8} in BEAF	\(f_{\omega^3 7+\omega^2 6+\omega5+4}(f_{\omega5+4}(4))\)
112	Ail sight out	\(f_{\varphi(4,0,0)}(\)\(\text{Never gonna let you down}\)\()\) in FGH	\(f_{\varphi(4,0,0)}(f_{\omega^{\omega^{68}}}(420))\)
113	Sail on, tough it	\(f_{\varphi(5,0,0)}(\)\(\text{Tomodachi}\)\()\) in FGH	\(f_{\varphi(5,0,0)}(f_{\omega^2 +\omega3}^{37}(22))\)
114	Iota light us	5I(Ten trying gammas) in Greek Letter Notation	\(f_{\omega^2 9}(f_{\omega^2 3}^5(4))\)
115	GFN prime charisma	(Largest GFN-262144)^(Largest GFN-524288) (currently (20866766²⁶²¹⁴⁴+1)^{(5897794⁵²⁴²⁸⁸+1)})^{[note 2]}	???
116	Unreasonable tepid	101,075	\(f_2(13)\)
117	Unusually long tetratri	(0,0,0,0)(1,1,1,1)(2,2,2,2)(3,3,3,3)[3] in BMS v4 (simulating Hardy hierarchy)	???
118	Basil wściekłość	1,273,262^2,623,721	\(f_2^2(20)\)
119	Bolognese sauce	{5,5,supertet,4,4} = {5,5,{4,4,4,4},4,4} in BEAF	\(f_{\omega^2 3+\omega4}(f_{\omega^2}(4))\)
120	Pasta logs hit suit	\(H_{\omega^{\omega^5}}(25)\) in Hardy Hierarchy	\(f_{\omega^5}(25)\)
121	Gumbo led to nth	145,321,457	\(f_2(23)\)
122	Bed log nth mu	10MM19 in Greek Letter Notation	\(f_{\omega^2 12}^{19}(10)\)
123	Aurum thumb	taz-79 = 79↑↑3 where taz-n means n↑↑3	\(f_2(f_2(492))\)
124	An Arrayed Dimensional Rung	{56,56[1[1[7]2]2]2} in BAN	\(f_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^6}}}}}}(56)\)
125	A limerick ref	{56,56[1\1\2]An Arrayed Dimensional Rung} in BAN	\(f_{\zeta_0 \omega}(f_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^6}}}}}}(56))\)
126	Cake life rim	{56,56[1[1¬ A limerick ref]2]2} in BAN (modified Hierarchial Hyper-Nested array version)	\(f_{\psi_0(\Omega_2 \omega)}(f_{\zeta_0 \omega}(f_{\omega^{\omega^{\omega^{\omega^{\omega^{\omega^6}}}}}}(56)))\)
127	Fast hoed alpha ski	10A(4!) = 10A24 in Greek Letter Notation	\(f_{\omega^2}^{24}(10)\)
128	Solutions to wreath bits	E200#^^#^^##(solution) in Extended Cascading-E notation	\(f_{\varphi(\zeta_0,0)}(f_{\omega+10}(f_{\omega+5}(f_{\omega+2}(f_{\omega+1}(42)))))\)
129	Solution to nice	cos(789°) = cos (69°) ~ 0.35836794^{[note 3]}	N/A
130	Victors Omen	79[1,1,1,1,1,2]79 in DeepLineMadom's array notation	\(f_{\omega^5}(79)\)
131	Novice storm	100[1{1 / 5}2]Victors Omen in DLMAN	\(f_{\varepsilon_3}(f_{\omega^5}(79))\)
132	Hold toughened	1000[1{1 `2` 1{1 / 2}2]79 in DLMAN	\(f_{\varphi(\omega,\varepsilon_0)}(79)\)
133	Mega beauty	\(f_{\omega^2}(10^6)\) in FGH	\(f_{\omega^2}(10^6)\) (exact)
134	Cool of duty^{[note 4]}	BB(12345)	Uncomputable naive extension
135	Kilo cool of duty^{[note 4]}	Rayo(cool of duty) (Rayo's function)	Uncomputable naive extension
136	Super cool of duty^{[note 4]}	Rayo(kilo cool of duty)	Uncomputable naive extension
137	Truth of dare^{[note 5]}	Defined as "the largest number defined using not more than corporal symbols in a K(corporal) system", using K(n) system, which can be described in not more than n symbols	Ill-defined, uncomputable, unformalised
138	Das Zulässige	\(f_{\zeta_{\omega}}(300)\) in FGH	\(f_{\zeta_{\omega}}(300)\) (exact)
139	Dopuszczalny	\(f_{\eta_{\omega}}(300)\) in FGH	\(f_{\eta_{\omega}}(300)\) (exact)
140	Held one through the admissable	\(f_{\Gamma_{\omega}}(300)\) in FGH	\(f_{\Gamma_{\omega}}(300)\) (exact)
141	Mega Penta	5[1,1,1,1,2]5 in DLMAN	\(f_{\omega^4}(5)\)
142	Super Mega Penta (also named S.M.Penta)	5[5{5}5]5 in DLMAN	\(f_{\omega^{\omega^4}4+4}(5)\)
143	Super Duper Mega Penta (also named S.D.M.Penta)	5[1{5,5,5,5,5}2]5 in DLMAN	\(f_{\omega^{\omega^{\omega^4 4+\omega^3 4 +\omega^2 4+\omega4+5}}}(5)\)
144	Overloaded Super Duper Mega Penta (also named O.S.D.M.Penta)	5[1{1,2/2}2]5 = 5[1{5/2}2]5 in DLMAN	\(f_{\varepsilon_0^{\omega^{\omega}}}(5)\)
145	Overflowed Overloaded Super Duper Mega Penta (also named O.O.S.D.M.Penta)	5[1{1`1`2}2]5 = 5[1{1/2}2]5 in DLMAN	\(f_{\varepsilon_0}(5)\)
146	Goodness Overflowed Overloaded Super Duper Mega Penta (also named G.O.O.S.D.M.Penta)	5[5<1/2>5]5 in DLMAN	\(f_{\Gamma_0 4+4}(5)\)
147	Extraordinarily Goodness Overflowed Overloaded Super Duper Mega Penta (also named E.G.O.O.S.D.M.Penta)	5[5{5//5}5]5 in DLMAN	\(f_{\varphi(\omega,3)^{\omega^5}4+4}(5)\)
148	Hyper Extraordinarily Goodness Overflowed Overloaded Super Duper Mega Penta (also named H.E.G.O.O.S.D.M.Penta)	5[5{5/////5}5]5 in DLMAN	\(f_{\varphi(\omega^5,3)^{\omega^5}4+4}(5)\)
149	Gasp Hyper Extraordinarily Goodness Overflowed Overloaded Super Duper Mega Penta (also named G.H.E.G.O.O.S.D.M.Penta)	5[1{1\2,2}2]5 in DLMAN	\(f_{\psi_0(\Omega_{\omega+1})}(5)\)
150	Googondo Gasp Hyper Extraordinarily Goodness Overflowed Overloaded Super Duper Mega Penta (also named G.G.H.E.G.O.O.S.D.M.Penta)	5[1{1\1\2}2]5 in DLMAN	\(f_{\psi_0(\Lambda)}(5)\)

Footnotes[]

↑ Using fundamental sequences associated to Extended Buchholz's function for the \(\psi\) function for the expression \(\psi_0\) and using fundamental sequences associated to Rathjen's psi function based on a weakly mahlo cardinal for the expression \(\psi_\Omega\).
↑ A dynamic googolism, as it changes over time.
↑ Irrational number.
↑ ^4.0 ^4.1 ^4.2 Naive extension of an uncomputable function.
↑ Ill-defined uncomputable number (see Oblivion and Utter Oblivion).

Sources[]

↑ AR Googol - Vast Irregulars of Goals numbers. Retrieved 2023-03-02 and 2023-12-26.

[:0-2] Using fundamental sequences associated to Extended Buchholz's function for the \(\psi\) function for the expression \(\psi_0\) and using fundamental sequences associated to Rathjen's psi function based on a weakly mahlo cardinal for the expression \(\psi_\Omega\).

[:1-3] A dynamic googolism, as it changes over time.

[irrational-4] Irrational number.

[naive-5] 4.0 ^4.1 ^4.2 Naive extension of an uncomputable function.

[oblivion-6] Ill-defined uncomputable number (see Oblivion and Utter Oblivion).

[1] AR Googol - Vast Irregulars of Goals numbers. Retrieved 2023-03-02 and 2023-12-26.

[1]

[note 1]

[note 2]

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[note 5]