Coogol

A coogol is equal to \(10^{100}\) using hypermathematics.Googol is a tiny dot, Hypermathematics 2009/02/12. retrieved 2022/03/10 The term was coined by googology101 on 2009/02/12. Hypermathematics is the same as normal mathematics except for one thing: addition is replaced by concatenation: 2+2=22 and 34+75=3475 for example.
A coogol is \((10^{2 \cdot 10^{99}+1} - 10)/99\) in normal notation and approximately E99.301#2 in Hyper-E Notation.
== Calculation ==
Hyper-E notation is used. ＋ is a normal notation. From \(m^n\) = \(m\cdot(E[m](n-1))\),Hypermathematics#Exponentiation
\(10^n\) = \(10 \cdot E(n-1)\) = \(\Sigma_{k=1}^{E(n-1)}E(k+k-1)\) = \((E(E(n-1)+E(n-1)+1) - 10)/99\)
Therefore \(10^n\) in hypermathematics is equal to \((10^{2 \cdot 10^{n-1}+1} - 10)/99\) in normal mathematics, and can be approximated by \(10^{2 \cdot 10^{n-1}-1}\).
From this result, a coogol is \((10^{2 \cdot 10^{99}+1} - 10)/99\) in normal notation and approximated as \(10^{2 \cdot 10^{99}-1} \approx 10^{10^{99.301}} = E99.301\#2 \).
== Approximation in other notations==
==Note==
Based on wrong calculation,Hypermathematics#Wrong calculation coogol was approximated as E20#99. It was corrected to E99.301#2 as described in the calculation section.
== Sources==
==See also==
Category:Numbers
Category:Even numbers
Category:Googol series
Category:Hypermathematics
Category:Numbers from A googol is a tiny dot
Category:Class 3
Category:Undulating numbers
ja:クーゴル
Category:Middle class 3