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The tetrofaxul is equal to 200!2 in Hyperfactorial array notation.[1][2] Tetrofaxul can be thought as "tetrofactorial" of 200, which is, by analogy with expofactorial, means \(f(n) = n \uparrow\uparrow (n-1) \uparrow\uparrow (n-2) \cdots 4 \uparrow\uparrow 3 \uparrow\uparrow 2 \uparrow\uparrow 1\). Thus, tetrofaxul can be represented as \(200 \uparrow\uparrow 199 \uparrow\uparrow 198 \cdots 4 \uparrow\uparrow 3 \uparrow\uparrow 2 \uparrow\uparrow 1\). This is based on tetration. The term was coined by Lawrence Hollom.

Etymology[]

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

Approximations in other notations[]

Notation Approximation
Hyper-E notation \(\textrm{E}153.90699754796802\#25\#197\)
Up-arrow notation between \(26 \uparrow\uparrow\uparrow 198\) and \(27 \uparrow\uparrow\uparrow 198\)
Chained arrow notation \(26 \rightarrow 198\rightarrow 3\)
BEAF \(\{26,198,3\}\)
Fast-growing hierarchy \(f_4(196)\)
Hardy hierarchy \(H_{\omega^4}(200)\)
Slow-growing hierarchy \(g_{\zeta_0}(200)\)
Tetrofaxul

A representation of the tetrofaxul

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
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