Changes: Grand Hugexul

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	\(\{200,\{200,2,201(\{X,X199,1,2\})2\},201(\{X,X199,1,2\})2\}\)^[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:

File:Grand Hugexul (Pronunciation).ogg

Sources

↑ Lawrence Hollom's large number site
↑ Using particular notation \(\{a,b (A) 2\} = A \&\ a\) with prime b.

[1] Lawrence Hollom's large number site

[2] Using particular notation \(\{a,b (A) 2\} = A \&\ a\) with prime b.

[1]

[2]

@@ Line 1: / Line 1: @@
-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]].<ref>[https://sites.google.com/a/hollom.com/extremely-big-numbers/home/hyperfactorial-numbers Lawrence Hollom's large numbers site]</ref>
+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>
-=== Number Navigator ===
+=== Etymology ===
+The name of this number is based on the word "'''grand'''" and the number "[[hugexul]]".
-{{numnav|Exahugexul|Grand Kilohugexul}}
+=== Approximations ===
+{| border="0" cellpadding="1" cellspacing="1" class="article-table" style="width: 600px;"
+|-
+! scope="col"|Notation
+! scope="col"|Approximation
+|-
+|[[Bird's array notation]]
+|\(\{200,\{200,2,201[1[1\neg3]200]2\},201[1[1\neg3]200]2\}\)
+|-
+|[[Bird's array notation#Hierarchical Hyper-Nested Arrays|Hierarchical Hyper-Nested Array Notation]]
+|\(\{200,\{200,2,201[1[1/2\sim2]200]2\},201[1[1/2\sim2]200]2\}\)
+|-
+|[[BEAF]]
+|\(\{200,\{200,2,201(\{X,X*199,1,2\})2\},201(\{X,X*199,1,2\})2\}\)<ref>Using particular notation \(\{a,b (A) 2\} = A \&\ a\) with prime b.</ref>
+|-
+|[[Fast-growing hierarchy]] (with [[List of systems of fundamental sequences#Fundamental_sequences_for_limit_ordinals_of_finitary_Veblen_function|this]] system of fundamental sequences)
+|\(f_{\Gamma_{198}+200}(f_{\Gamma_{198}+199}(200))\)
+|-
+|[[Hardy hierarchy]] (with [[List of systems of fundamental sequences#Fundamental_sequences_for_limit_ordinals_of_finitary_Veblen_function|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:
+[[File:Grand_Hugexul_(Pronunciation).ogg|center]]
 === Sources ===
 <references/>
@@ Line 9: / Line 36: @@
 [[Category:Numbers by Lawrence Hollom]]
 [[Category:Factorial numbers]]
-[[Category:Higher array notation level]]
+[[Category:Powers of 200]]
+[[Category:Bachmann's collapsing level]]