Googology Wiki
Advertisement
Googology Wiki

View full site to see MathJax equation

The hyperfaxul (also called ducenfaxul) is equal to 200!200 or 200![1] using Hyperfactorial Array Notation. In Jonathan Bowers' bracketed operator notation it can be expressed as \(200\{200\}199\{200\}198\{200\}\cdots\{200\}4\{200\}3\{200\}2\). The term was coined by Lawrence Hollom.[1]

Etymology[]

The name of this number is based on prefix "hyper-" and the number "faxul".

Approximations in other notations[]

Notation Approximation
Arrow notation \((3 \uparrow^{199} 3) \uparrow^{201} 198\)
Hyper-E notation \(\textrm E10\#\#201\), \(\textrm E3638334640023.7783\#7625597484984\#1\#\underbrace{2\#2\#2\cdots2\#2\#2}_{\text{196 2's}}\#1\#198\)
Chained arrow notation \((3 \rightarrow 3 \rightarrow 199) \rightarrow 198 \rightarrow 201\)
BEAF \(\{\{3,3,199\},198,201\}\)

Fast-growing hierarchy

\(f_\omega(202)=f_{202}(202)\)
Hardy hierarchy \(H_{\omega^{\omega}}(202)\)
Slow-growing hierarchy \(g_{\varphi(201,0)}(200)\)

Sources[]

See also[]

Hyperfactorial array notation numbers: Minor Faxul Group | Major (Giaxul)

Faxul group: Faxul (Kilo- · Mega- · Giga- · Tera- · Peta- · Exa- · Grand (Kilo- · Mega- · Giga- · Tera- · Peta- · Exa-) · Bigrand (Kilo- · Mega-) · Trigrand (Kilo-) · Quadgrand · Quintgrand)
Expofaxul group: Expofaxul (Kilo- · Mega- · Giga- · Tera- · Peta- · Exa- · Grand (Kilo- · Mega- · Giga- · Tera- · Peta- · Exa-) · Bigrand (Kilo- · Mega-) · Trigrand (Kilo-) · Quadgrand · Quintgrand)
Tetrofaxul group: Tetrofaxul (Kilo- · Mega- · Giga- · Tera- · Peta- · Exa- · Grand (Kilo- · Mega- · Giga- · Tera- · Peta- · Exa-) · Bigrand (Kilo- · Mega-) · Trigrand (Kilo-) · Quadgrand · Quintgrand)
Pentofaxul group: Pentofaxul (Kilo- · Mega- · Giga- · Grand (Kilo- · Mega- · Giga-) · Bigrand · Trigrand)
Hexofaxul group: Hexofaxul (Kilo- · Mega- · Giga- · Grand (Kilo- · Mega- · Giga-) · Bigrand · Trigrand)
Heptofaxul group: Heptofaxul · Octofaxul
Hyperfaxul group: Hyperfaxul (Kilo- · Mega- · Giga- · Tera- · Peta- · Exa- · Grand (Kilo- · Mega- · Giga- · Tera- · Peta- · Exa-) · Bigrand (Kilo- · Mega-) · Trigrand (Kilo- · Mega-) · Quadgrand · Quintgrand)
Redstonepillager's extensions: Dopperfaxul · Googaxul
Advertisement