Schmittyillion

Schmittyillion is a number coined by Trakaplex when attempting to coin the largest googolism ending in "illion".Trakaplex, a comment to "What is the biggest known number?" in Answers.com. It has two different definitions coined over time, the original one in 2021, and the most recent one in 2023.
== Original definition ==
The original definition of schmittyillion was introduced as "10^310^310... a googol minus 2 more times raised to the 4182001". It is intended to be a tier googol illion with respect to Bower's system, which has never been used, according to the creator. It was first clarified on Googology Testing WikiSchmittyillion in Googology Testing Wiki., but the defining formula included undefined convention on brackests and was based on a misconception of the behaviour of tetration.Trakaplex, Emphasizing Schmittyillion, Googology Wiki user blog. (The creator showed a little ambiguous expression in the blog post, and noticed a misconception in a comment.) Later, it was mentioned to on a new answers.com post asking the "biggest known number in the world", but the description was ambiguous, too. Finally, the creator clarified the precise definition, as we will show in "Explanation" section. The complexity couldn't simply be written in simple notation. 
=== Issue ===
It was unknown what the original definition "10^310^310... a googol minus 2 more times raised to the 4182001" precisely meant when the original definition was posted. Later, the creator explained it as \(10^{^{13}3\times10^{3,000}+3}\), which is still ambiguous.
Finally, the creator explained that this number is expressed in the following way:A difference page of the talk page of this article. (The creator showed a clearer expression.)
: 103*103*103*103*10....(a googol of these 3*10's)4182001(back down)+3
Although it includes ellipsis, it looks clearer than the original description.
=== More graphic Definition ===
\(10^{\underbrace{3\times 10^{.^{.^{.^{3\times 10^{4182001}}}}}}_{10^{100}\quad 3\times 10's} + 3}\)
This still has ellipses, but it is easier to see what is likely meant.
== Alternative definitions ==
Considering the creator's explanations, the intended value of the number is perhaps given as \(10^{a_{\textrm{googol}}+3}\) using the sequence \((a_n)_{n=1}^{\infty}\) defined in the following recursive way:
# If \(n = 1\), then \(a_n := 3 \times 10^{4182001}\)
# If \(n > 1\), then \(a_n := 3 \times 10^{a_{n-1}}\)
== 2023 Definition ==
According to a recent source, the newest definition is 10↑(3*10↑(3*10↑↑googol-1↑(4182001))+3).https://brettzotij.blogspot.com/2023/03/i-killillion-zillion.html (retrieved 4th March, 2023)
=== Approximations ===
== Etymology ==
It is based off 'Schmitty Winkleson' and the word 'illion'.
== See also ==
== Sources ==
Category:Numbers
Category:Numbers by Trakaplex
Category:Illion
Category:Tetration level