INTRODUCTION
Welcome to my website on large numbers. Here, I cover two main topics: numbers in general and very large numbers. This site aims primarily to cover the wonderful world of large numbers, with their history, naming, and how to make large numbers.
If you think that there isn't anything to say about large numbers besides the googol and googolplex and infinity, you are sorely mistaken. First off, forget about infinity. Since infinity is by definition larger than any finite number, putting infinity into the large number discussion is cheating, and nobody likes cheaters.
As for the googol and googolplex, most of the numbers I will discuss will leave the googol and googolplex in the dust! Don't believe me? Have a look at some of my articles. And if you believe forming large numbers is very easy (e.g. just write more and more zeros), you are once again wrong. As you go higher and higher through large numbers, you will find that they gradually get harder and HARDER and HARDER to devise! Once again, if you don't believe me just look at some of my articles.
The subject of large numbers, thanks to a mysterious figure named "Andre Joyce", is most often referred to as googology. The name is known mostly through its use in the name of Googology Wiki, a wiki devoted to the subject of large numbers. Googology is focused both on devising large numbers for their own sake, and their use in serious mathematics. Numbers with such use go a lot further through the world of numbers than you probably think—if you're thinking Graham's number is the largest "useful" number, then you're absolutely wrong. There's a few words derived from "googology" which I'll use a lot in this site: a person who studies googology is known as a googologist; a mathematical object relevant to googology (a function, notation, number, etc) is called a googologism; and the term googolism is similar but applies only to numbers, more specifically names for numbers.
A question you may have: Why study or learn about large numbers? I'll borrow an argument Lawrence Hollom used on the homepage of his old site (source): Is there a reason we do things like read a novel or go to an art museum, if we're not going to get much useful out of it? No, but we still do because we enjoy doing those kinds of things. Therefore, does there need to be a reason to read about ridiculously large numbers other than because you want to? I think not.
Now about the site itself: how is this site intended to be read?
My site is divided into several sections, and each section consists of articles. Some of the articles which cover multiple related topics are further divided into sub-sections. As for the order, the numbered sections are designed to be read in order of articles, while the supplemental section (section L) can be read in pretty much whatever order you want. If you're already experienced with large numbers, I hope this site still provides a good insight into my own views on very large numbers.
But why did I make this site?
There are plenty of other sites on the Internet regarding large numbers, so why make another? Originally I planned for this site to mostly only cover large number-related stuff others haven't bothered to review such as Andre Joyce's googo- and googolple- naming system, as well as give a "semi-comprehensive" (as I dub it) list of numbers. That kind of stuff was all I really had in mind for this site when I launched it on May 28, 2014. However, after several months I began to view this site as more and more of a coverage of most large numbers out there, which is why I revamped this site's design on October 2-3, 2014. (The site's current design came about May 28, 2022, for the site's eighth anniversary and move to the new Google Sites, but the content is organized about the same.)
Now this site aims to give a coverage of any and all large numbers I find to be significant, ranging from the famous things like googolplex and Graham's number to the obscure and esoteric corners of very large numbers. But why? Haven't lots of other people covered those things? Yes, but I still chose to cover these areas for two reasons: (1) I aim to give my own specific insight on these large numbers, and (2) I want to cover content in a way that's accessible to beginners. A lot of the topics I cover or plan to cover aren't really extensively discussed in very many other places, such as Hollom's hyperfactorials or many of Joyce's naming systems.
As I said earlier, this website is divided into several sections. The first starts off with an introduction to the numbers as we know them, along with their size, naming, and some other nearby-sized numbers like the googol and googolplex. The second section leaves the first section's numbers in the dust with things like Knuth's up-arrows and Graham's number, sorted roughly by size of numbers. Then the third section discusses some of the lesser-known googology (which, incidentally, is a lot more interesting) such as Bowers' arrays, Sbiis Saibian's named numbers, and fast-growing sequences like the Kirby-Paris hydra. Further sections will be added as this site grows, with more and more advanced googology as you progress through the sections.
There's also a supplemental section, section L (short for "list"), used for any and all pages intended to list things. In that part you'll find a very long work-in-progress 7-part list of numbers, along with some supplementary lists and a timeline of googology. You can jump to section L whenever you please, but once again, many (but not all) parts require understanding of previously covered material.
That's about all I have to say for the introduction to this site. So what are you waiting for? Go back to the home page to start navigating this site.