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− | The '''Grand Hugexul''' is equal to |
+ | The '''Grand Hugexul''' is equal to ((...((200![200(1)200])![200(1)200])![200(1)200]...)![200(1)200])![200(1)200] (with [[hugexul]] parentheses), using [[Hyperfactorial array notation]]. The term was coined by [[Lawrence Hollom]].<ref>[https://sites.google.com/a/hollom.com/extremely-big-numbers/old-homepage/hyperfactorial-numbers/number Lawrence Hollom's large number site]</ref> |
=== Etymology === |
=== Etymology === |
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The name of this number is based on the word "'''grand'''" and the number "[[hugexul]]". |
The name of this number is based on the word "'''grand'''" and the number "[[hugexul]]". |
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|\(\{200,\{200,2,201(\{X,X*199,1,2\})2\},201(\{X,X*199,1,2\})2\}\)<ref>Using particular notation \(\{a,b (A) 2\} = A \&\ a\) with prime b.</ref> |
|\(\{200,\{200,2,201(\{X,X*199,1,2\})2\},201(\{X,X*199,1,2\})2\}\)<ref>Using particular notation \(\{a,b (A) 2\} = A \&\ a\) with prime b.</ref> |
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+ | |[[Fast-growing hierarchy]] (with [[List of systems of fundamental sequences#Fundamental_sequences_for_limit_ordinals_of_finitary_Veblen_function|this]] system of fundamental sequences) |
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− | |[[Fast-growing hierarchy]] |
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− | |\(f_{\Gamma_{198}+200}(200)\) |
+ | |\(f_{\Gamma_{198}+200}(f_{\Gamma_{198}+199}(200))\) |
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+ | |[[Hardy hierarchy]] (with [[List of systems of fundamental sequences#Fundamental_sequences_for_limit_ordinals_of_finitary_Veblen_function|this]] system of fundamental sequences) |
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− | |[[Hardy hierarchy]] |
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− | |\(H_{\Gamma_{198}\omega^{200}}(200)\) |
+ | |\(H_{\Gamma_{198}\omega^{200}+\Gamma_{198}\omega^{199}}(200)\) |
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|[[Slow-growing hierarchy]] |
|[[Slow-growing hierarchy]] |
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|\(g_{\theta(\Omega_2+\varphi(\Omega_2,199)+200,\vartheta(\Omega_2+\varphi(\Omega_2,199)+199))}(200)\) |
|\(g_{\theta(\Omega_2+\varphi(\Omega_2,199)+200,\vartheta(\Omega_2+\varphi(\Omega_2,199)+199))}(200)\) |
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+ | ==Pronunciation== |
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− | |||
+ | It is likely pronounced as so: |
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− | === Number Navigator === |
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+ | [[File:Grand_Hugexul_(Pronunciation).ogg|center]] |
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− | {{numnav|Exahugexul|Grand Kilohugexul}} |
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=== Sources === |
=== Sources === |
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<references/> |
<references/> |
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[[Category:Numbers by Lawrence Hollom]] |
[[Category:Numbers by Lawrence Hollom]] |
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[[Category:Factorial numbers]] |
[[Category:Factorial numbers]] |
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− | [[Category: |
+ | [[Category:Powers of 200]] |
+ | [[Category:Bachmann's collapsing level]] |
Revision as of 02:36, 26 December 2020
The Grand Hugexul is equal to ((...((200![200(1)200])![200(1)200])![200(1)200]...)![200(1)200])![200(1)200] (with hugexul parentheses), using Hyperfactorial array notation. The term was coined by Lawrence Hollom.[1]
Etymology
The name of this number is based on the word "grand" and the number "hugexul".
Approximations
Notation | Approximation |
---|---|
Bird's array notation | \(\{200,\{200,2,201[1[1\neg3]200]2\},201[1[1\neg3]200]2\}\) |
Hierarchical Hyper-Nested Array Notation | \(\{200,\{200,2,201[1[1/2\sim2]200]2\},201[1[1/2\sim2]200]2\}\) |
BEAF | \(\{200,\{200,2,201(\{X,X*199,1,2\})2\},201(\{X,X*199,1,2\})2\}\)[2] |
Fast-growing hierarchy (with this system of fundamental sequences) | \(f_{\Gamma_{198}+200}(f_{\Gamma_{198}+199}(200))\) |
Hardy hierarchy (with this system of fundamental sequences) | \(H_{\Gamma_{198}\omega^{200}+\Gamma_{198}\omega^{199}}(200)\) |
Slow-growing hierarchy | \(g_{\theta(\Omega_2+\varphi(\Omega_2,199)+200,\vartheta(\Omega_2+\varphi(\Omega_2,199)+199))}(200)\) |
Pronunciation
It is likely pronounced as so:
Sources
- ↑ Lawrence Hollom's large number site
- ↑ Using particular notation \(\{a,b (A) 2\} = A \&\ a\) with prime b.
See also
Faxul · Giaxul · Hugexul · Enormaxul · Destruxul · Extremexul · Gigantixul · Nucleaxul · BIGG
Hugexul group: Hugexul · Kilohugexul · Megahugexul · Gigahugexul · Terahugexul · Petahugexul · Exahugexul · Grand Hugexul · Grand Kilohugexul · Grand Megahugexul · Grand Gigahugexul · Grand Terahugexul · Grand Petahugexul · Grand Exahugexul · Bigrand Hugexul · Bigrand Kilohugexul · Bigrand Megahugexul · Trigrand Hugexul · Trigrand Kilohugexul · Trigrand Megahugexul · Quadgrand Hugexul · Quintgrand Hugexul · Superior Hugexul · Superior Kilohugexul · Superior Megahugexul · Superior Gigahugexul · Superior Grand Hugexul · Superior Grand Kilohugexul · Superior Grand Megahugexul · Superior Grand Gigahugexul · Superior Bigrand Hugexul · Superior Trigrand Hugexul · Bisuperior Hugexul · Bisuperior Kilohugexul · Bisuperior Megahugexul · Bisuperior Gigahugexul · Bisuperior Grand Hugexul · Bisuperior Grand Kilohugexul · Bisuperior Grand Megahugexul · Bisuperior Grand Gigahugexul · Bisuperior Bigrand Hugexul · Bisuperior Trigrand Hugexul
Hugebixul group: Hugebixul · Kilohugebixul · Megahugebixul · Gigahugebixul · Grand Hugebixul · Grand Kilohugebixul · Grand Megahugebixul · Grand Gigahugebixul · Bigrand Hugebixul · Trigrand Hugebixul · Superior Hugebixul · Superior Kilohugebixul · Superior Megahugebixul · Superior Grand Hugebixul · Superior Grand Kilohugebixul · Superior Grand Megahugebixul · Superior Bigrand Hugebixul · Bisuperior Hugebixul · Bisuperior Kilohugebixul · Bisuperior Megahugebixul · Bisuperior Grand Hugebixul · Bisuperior Grand Kilohugebixul · Bisuperior Grand Megahugebixul · Bisuperior Bigrand Hugebixul
Hugetrixul group: Hugetrixul · Kilohugetrixul · Megahugetrixul · Gigahugetrixul · Grand Hugetrixul · Grand Kilohugetrixul · Grand Megahugetrixul · Grand Gigahugetrixul · Bigrand Hugetrixul · Trigrand Hugetrixul · Superior Hugetrixul · Superior Kilohugetrixul · Superior Megahugetrixul · Superior Grand Hugetrixul · Superior Grand Kilohugetrixul · Superior Grand Megahugetrixul · Superior Bigrand Hugetrixul · Bisuperior Hugetrixul · Bisuperior Kilohugetrixul · Bisuperior Megahugetrixul · Bisuperior Grand Hugetrixul · Bisuperior Grand Kilohugetrixul · Bisuperior Grand Megahugetrixul · Bisuperior Bigrand Hugetrixul
Hugequaxul group: Hugequaxul · Kilohugequaxul · Megahugequaxul · Gigahugequaxul · Grand Hugequaxul · Grand Kilohugequaxul · Grand Megahugequaxul · Grand Gigahugequaxul · Bigrand Hugequaxul · Trigrand Hugequaxul · Superior Hugequaxul · Superior Kilohugequaxul · Superior Megahugequaxul · Superior Grand Hugequaxul · Superior Grand Kilohugequaxul · Superior Grand Megahugequaxul · Superior Bigrand Hugequaxul · Bisuperior Hugequaxul · Bisuperior Kilohugequaxul · Bisuperior Megahugequaxul · Bisuperior Grand Hugequaxul · Bisuperior Grand Kilohugequaxul · Bisuperior Grand Megahugequaxul · Bisuperior Bigrand Hugequaxul