Metillion

Metillion is equal to \(10^{3\times 10^{3\times 10^{3\times 10^{45}}} + 3}\)Extended Tier 4 to 6 illions or \(10^{3\times 10^{3\times 10^{3\textrm{ quattuordecillion}}} + 3}\) using the short scale definition of quattuordecillion. The term was coined by CompactStar (formerly known as Nirvana Supermind) as the smallest in the part of his unofficial extension of Bower's -illion system which ended at multillion. 
YouTube user BAT4423【Googology Bat】 coined pyrillion as an alternative name for this number.-illion Numbers V2 Part.1 (Tier 1 ~ Tier 4) - YouTube (retrieved August 2 2022) 
==Etymology==
This name is derived from the suffix -illion and the name metaverse.
== Approximations==
Notation 	Expression
Scientific Notation 	\(10^{3\cdot 10^{3\cdot 10^{3\cdot 10^{45} } } } \) (exact)
Up-arrow notation 	\(10 \uparrow (3 \times (10 \uparrow (3 \times (10 \uparrow (3\times 10\uparrow 45))))+3)\) (exact)
Chained arrow notation 	\(10 \rightarrow (3 \times (10 \rightarrow (3 \times (10 \uparrow (3\times 10\rightarrow 45))))+3)\) (exact)
H* function 	H(H(H(H(14)-1)-1))
BEAF 	\(\{10,\{3\times \{10,3 \times \{10,3\times\{10,45\}\}\}+3\}\}\)
Munafo's ASCII-lexicographic ordering	p3_e045_3
Fast-growing hierarchy 	\(f^4_2(146)\)
==Sources==
==See also==
*Zillion Notation
*Extensible Illion System
Category:Numbers
Category:Class 5
Category:Illion
Category:Tier 4 -illion numbers
Category:Numbers and functions by CompactStar