Large Numbers

One to Infinity: 

A Guide to the Finite  

( alpha 2.0.0.0.5 )

A Web Book on Large Numbers

by Sbiis Saibian

            Welcome to my Large Number Site. Here you will find the contents of my perpetually incomplete "One to Infinity: A Guide to the Finite", a web book devoted entirely to the subject of large finite numbers.

            If you're a newcomer check out the "INFORMATION DESK" for basic information about content and navigation. 

            To the right you will find the "Updates and Announcements Panel". Any major changes or additions to the site are made note of here, and quick links to new content areas are provided. 

            Below you will find links to the main content of my web book, which includes all currently available chapters and an appendix. If you would like to communicate with the author, or would like to know more about site activity, check out the "Communications Center" at the bottom of the page.

Disclaimer

Preface

SECTION I

 Numeric Fundamentals

    I introduce the counting numbers and how we can define, name, and notate them. Next we learn the basics of how to manipulate these numbers, what properties they possess and how we can show that one is larger than another. Armed with these fundamentals we will then consider the kinds of numbers people usually mean when they say it is very large.

1.1 - The Nature of Number

1.2 - Systems of Numeration & Naming Conventions

1.3 - Fundamentals of Arithmetic (ON HIATUS)

1.4 - Properties of the Counting Numbers (ON HIATUS)

1.5 - Encyclopedia of Numbers 

SECTION II

The Gargantuan, The Astronomic, & The Phantasmal  

        We now explore some astronomical numbers that occur in physics and cosmology. Although vast these numbers are no less real than the numbers we encounter day to day. We then consider even more fantastic numbers that only exist in the human imagination (as far as we know)...

2.1 - Cosmic Horizons

2.2 - The SI Prefixes

2.3 - Giants of Antiquity & the Mind

2.4 - The -illion Series

SECTION III 

Introduction to Recursive Methods

        We begin a more formal treatment of the basic concepts. Using more formal approaches we will be able to overcome previous impediments and begin generating numbers much larger than anything yet constructed in the previous two sections. We will also be going over all the more popular notations for "extremely large" numbers. Prepare to blast off towards infinity !!! 

3.1 - Introduction to Recursive Functions

3.2 - Some Elementary Large Number Notations

3.3 - Large Number Arithmetic

SECTION IV

Intermediate Googology :

A Theory of Super Structures

        We now move beyond the popular discussion of large numbers and develop a general theory of recursive notation. We will then explore our own limits with recursive methods. We will also be introduced to many higher level topics in googology: array notation, ordinal notations, the fast-growing hierarchy, and many new ideas for handling these topics. Amateur hour is over ... we now will start treading over into the professional mathematician's territory!

4.1 - The Astounding Work of Jonathan Bowers

4.2 - The Fast Growing Hierarchy

4.3 - Extensible-E

4.4 - Towards a New Theory of Googology (ON HIATUS)

4.5 - Comparing Systems (ON HIATUS)

SECTION V

(ON HIATUS)

APPENDIX

        Read everything and want to learn more ? This last "section" provides additional information, tables, charts and links to other large number sites.

A.1 - THE APPENDICES

INDEX

        Check out the new Index feature for quick reference to specific topics you are looking for!

I.1 - INDEX

COMMUNICATIONS 

CENTER

           Curious about what's coming up next? Have a question you'd like to ask? You've come to the right place. The communications Center (Com Center for short) is a place where I can talk about planned developments for the site and future goals, and it also provides the opportunity for feedback and questions.

C.1 - COMMUNICATION CENTER