A Guide to Factorial
From humble beginning to the finity
A Googology system employs the use of factorial-like notation
When I was in highschool, I have a weird fascination towards big number. At that time, I didn't know any big number, even the "smaller" one like Graham Number, let alone "bigger" one like TREE(3),Busy Beavers, Aeckerman's Arrow Notation, Conway's Arrow Notation, BEAF Notation, fast-growing hierarchy function, etc. Long story short, I found Googology Wikia and I learn so much things there (and of course I didn't understand 99% of what I've read). I also start to binge watching David Metzler's "Large Number" lecture series and learning ordinal number.
Since there are few Googology that use factorial-like notation, I have an urge to write a system of notation that employs factorial. I didn't plan this Googology system to be stronger than other noation. Of course not. I can't understand majority of Sbiis Sabian's notation (Extensible-E Notation), let alone to surpass him. I also didn't understand fast growing hierarchy beyond the 𝜀0 level. I write this purely to excerices my understanding at recursive function and diagonalization, and for fun.
You can read it here