Extremely Large Numbers

Attempting to define some of the most stupidly large numbers ever.

Why? Why not!

Welcome to my site on large numbers, or googology as it is also known. If you're wondering why this website exists, and why anyone would make this, and the answer 'because it's fun' isn't good enough, then you're probably in the wrong part of the internet for you. Here you can (occasionally) find some webpages about large numbers, some of which I came up with, some of which I did not. Currently, they mainly discussing my notation in a little detail, and contain a large number of large numbers. Hopefully at some point the website will contain information on the work of other googologists, and be free from pages which have said "page under construction" or "coming soon" for a length of time considerably longer than what could possibly be described as "soon" (see my old website, stored here for many examples of this). I am currently in the process of completely revamping my old notation into a (sort of) all new, more powerful notation, starting with Factorial Array Notation: FAN. Firstly, though, we can look at the fast-growing hierarchy (FGH).

Section 1: The Fast-Growing Hierarchy

An overview of the the FGH, especially the larger end of the spectrum, to allow for ordinals to compare my notation to.
The FGH and small ordinals: how the hierarchy itself works, and some smaller ordinals to demonstrate these ideas.
Ordinal collapsing functions and very large ordinals: an overview of the larger ordinals in the spectrum, and how they are produced using ordinal collapsing functions.

Section 2: Factorial Array Notation

Now, onto the new stuff. This is a full explanation of my Factorial Array Notation (FAN). This is something I've been working on, on and off, for a few years, and I can almost guarantee it will never reach a state of being finished.
Introduction to factorial numbers
Factorial Array Notation: Climbing into the numerical stratosphere.
Extended Factorial Array Notation: This isn't anywhere near complete yet, but I'm just going to put the links in to what's there so far.

Section 3: Comparing Systems

Now that we actually have a system to generate large numbers, we need to actually find something to do with it. Luckily there are plenty of other systems that mine can be compared to, to see how it actually performs against other similarly insane systems.
FAN against BEAF: comparing my system to one of the most well known of all the googological systems: BEAF, or Bowers' Extended Array Notation. This is currently under development.

Section 4: Uncomputable Functions

A look at some googological functions I did not come up with, but that I have worked on bounding:
Rado's Σ Function: developed by Rado, and based on the work of Alan Turing, and the original uncomputable function. Also, work-in-progress on the proof of the value of Σ(5). Coming soonish. Possibly. But probably not.
The Ξ Function: Made by Adam P. Goucher, and is one of the fastest growing functions ever. Also, some original lower bounds on the function.
Introducing the all new doodle function! An original creation that may be appearing at some point!

COPYRIGHT © Lawrence Hollom 2014