Preface
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Prerequisites
What you need to Know
This website is designed in the hopes that anyone with a high school education can eventually learn and understand most of the material. A basic understanding of high school mathematics is assumed. Constructing large numbers requires a well ordered mathematical system. There is no getting around this fact. Mathematics is absolutely fundamental to the study of large numbers. Because of this most people assume they need to study advanced mathematics for years before they can even begin to understand large numbers. This is simply not true. In fact the subject of large numbers is relatively intuitive and anyone can begin as long as they have some fundamental grasp of the concept of numbers. All you really need is a starting point, and some basic rules of extension. The game of large numbers then becomes, how far can you extend your system before madness or confusion, or both, overtake you. Of coarse we will also want to be able to compare systems of various "players" so that people can contribute and compete in the large number game. This is where proof and analysis come in. Admittedly this does require a greater level of sophistication, but anyone can at least begin imagining large numbers. All it requires is a little knowledge, willingness, and a whole lot of imagination :)
That being said some basic familiarity with mathematical concepts is recommended. You should at least have a good grasp of number concepts, basic operations, and a basic understanding of some algebraic concepts. Algebra is of particular importance to our subject because the secret to generating large numbers is really repeat substitution as we will see later. You don't need to know Calculus to understand this material. In fact we will almost always be working within a "discrete" framework. This just means we will be discussing systems which are finite and which are made of distinct and countable objects instead of continuous quantities. If you have taken a pre-Calculus course and are familiar with the concepts of functions, recursive formulas, and inductive proof that will certainly be of service to you here, but it is not absolutely necessary as I will develop all of these ideas from notions of algebra. We will have little to no use for graphs here since most of the functions grow far too rapidly, and are discrete rather than continuous. Even if your a little shaky with your algebra and arithematic don't fret. I will be going over all of the basics in the first section. All you really need to understand is the concept of numbers and elementary arithmetic. I will do my best to explain the rest.
It should be noted that our primary focus will be large numbers in and of themselves, not mathematics in it's entirety. Instead we will be using mathematics as the means to an end, that end being generating and studying large numbers. Basically we will borrow from various fields of mathematics when it is convenient to do so. We will touch on many subject only tangentially related to large numbers such as logic, set theory, theory of algorithms, proof, mathematical foundations, but all of this will ultimately go towards constructing larger and larger numbers. Start thinking of math as a conceptual tool, rather than an obstacle. The obstacle will be tackling complexity and disorder, and mathematics will be the tool we use to combat this.
How to Navigate this Site
This website is better understood as a "Web book". It's format is not that different from your typical math textbook. It is built of several "Sections" (or Units) which are broken down further into chapters. Each chapter then breaks down into individual articles, which are actually the web pages that make up the bulk of the real content of the site.
There are essentially three levels of navigation. The highest level of navigation is the homepage. It contains links to every chapter and allows you to choose any one at will. The homepage also includes additional links which lead to additional content outside of the "book" content. There is also a side bar on the homepage which lists updates and announcements in chronological order starting with the most recent.
Once your "within a chapter" you are navigating within the second level. Each chapter is like a mini-table of contents. It provides links to articles and provides a brief description of the content of each. Every chapter includes a link back to the homepage at the top and bottom of the web page. You can also navigate to any other chapter via the chapter links located at the left. You can therefore navigate the site entirely without having to return to the homepage.
The lowest level of navigation is the articles. Each article allows you to return to the home page or chapter page at the top and bottom. In addition you can jump to the previous and next article via links at the top and bottom. The only catch is you can not navigate articles across chapter boundaries. To get to the next chapter, you have to go back to the chapter page and use it to navigate to the next chapter. The reason for this is because articles are written within the context of the established chapter, and jumping across chapters might otherwise be confusing.
There is also a forth level, but I try to use it sparingly. Sometimes a I will want to discuss a sub-topic which is not worthy of a full blown article. In this case an article may contain a link to a sub-article. Sub-articles contain the usual link to the home page, but they do not let you navigate to any other level than back to the original article.
In the future I may implement other navigational means so that users can find specific content more easily. For example I might create an index page which allows you to navigate the site by content. But the primary structure of sections, chapters and articles will always be there.
Because the subject of large numbers is essentially accumulative it is recommended you read content in order. However if you are already familiar with some of the fundamentals you can of coarse skim, or skip at your choosing. I also don't want this to be treated like a textbook. Think of it more as an instruction manual to large numbers. You can read it as religiously or casually as you like.
Note: You can check out the progress link on the homepage for a quick report on how far the site is towards completion.
In any case I hope that you will find this website a valuable resource and an enjoyable read :)
Sincerely,
-- Sbiis Saibian
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