The Pointless Gigantic List Database

https://sites.google.com/site/pointlesslargenumberstuff/home/l



BIG FOOT
FOOT10(10100)


BIG FOOT is currently honored as the largest named number. It was defined by LittlePeng9 of Googology Wiki using something called first-order oodle theory (FOOT for short), a generalization and extension of first-order set theory. The name was suggested by Sbiis Saibian. It was developed in a Googology Wiki blog post, and then Nathan Ho decided to publish it on an article in his own personal website, with a few additions (mainly on the background of Rayo's number and extensions to the number).


First order oodle theory is like the set theory used to define Rayo's number, but augmented with the symbols [ and ]. With just those two symbols we can generate numbers vastly larger than any other extension to FOST people have yet devised (and all those other extensions are quite naive). With FOOT, we can define a function FOOT(x) as the largest number expressible with x symbols in FOOT, and with the FOOT function LittlePeng9 defined the monstrous number FOOT10(10100) (the superscript 10 denotes how many times FOOT(x) is applied to 10100).


Why is BIG FOOT honored as the largest named number while other extensions like Fish number 7 weren't? Because it was not a naive extension like the other extensions to Rayo's number (arguably this includes Fish number 7). Naive extensions are the best way to embarrass yourself in front of googologists, because anyone could come up with them, while the same cannot be said for coming up with numbers like Rayo's number, BIG FOOT, or even just Graham's number.


And that brings us to an important point: googology is not so much about finding the largest number as it is about continually finding better ways to make large numbers. As Nathan Ho once said, "googology is a never-ending quest to outrun itself".