Pentation? How quaint. For other Large Number fans, David Metzler has a wonderful playlist that goes way down the rabbit hole of the fast growing hierarchy:
Almost all of these mind-bogglingly large numbers are built around recursion, like the Ackermann function, which effectively has an argument for the number of Knuth up arrows to use. Then you can start thinking about feeding the Ackermann function into that slot and enjoy the sense of vertigo at how insane that becomes.
I find it fascinating how quickly the machinery of specifying large numbers probes the limits of what's definable within the mathematical systems we use.
https://www.youtube.com/playlist?list=PL3A50BB9C34AB36B3
Highly recommended.
Almost all of these mind-bogglingly large numbers are built around recursion, like the Ackermann function, which effectively has an argument for the number of Knuth up arrows to use. Then you can start thinking about feeding the Ackermann function into that slot and enjoy the sense of vertigo at how insane that becomes.
I find it fascinating how quickly the machinery of specifying large numbers probes the limits of what's definable within the mathematical systems we use.