One to Infinity: A Guide to the Finite ( alpha 1.9.7.16.1 )
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. 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.
1.3 - Fundamentals of Arithmetic (ON HIATUS)
1.4 - Properties of the Counting Numbers (ON HIATUS)
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)...
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!
4.4 - 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. INDEX Check out the new Index feature for quick reference to specific topics you are looking for! 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. Quetzalcoatl | UPDATES & ANNOUNCEMENTS 2017.02.08 2017 Renewal Plan. New Announcement. See here. 2017.01.26 "Vanishing Point" Image posted on homepage 2017.01.05 New Introduction for "One to Infinity". 2017.01.04 Site officially Reactivated. New Announcement. See here. 2017.01.01 Happy New Year's to the world 2016.12.25 Merry Christmas to the Googology Community! 2016.12.13 Introducing the "Decimice". Find in Appendix F. 2016.12.09 Happy 8th Anniversary to the LNS! 2016.11.28 Today is exactly halfway between Halloween and Christmas. Merry Christhallowas! 2016.10.25 USNL and ULNL are fused to form the UFNL. 2016.10.19 All currently known perfect numbers added to ULNL. 2016.10.11 All currently known mersenne primes added to ULNL 2016.10.10 Book Disclaimer added 2016.09.10 - 2016.09.21 Site disabled (est. time) 2016.08.12 Site once again reactivated 2016.08.11 Site temporarily disabled and rendered unavailable 2016.01.02 2016.01.01 Happy New Year!!! 2015.12.25 Merry Christmas!!! 2015.12.09 Today marks the 7th Anniversary of the LNS 2015.08.07 New preface written for book. 2015.08.06 Version History has been added to the Information Desk 2015.08.04 New Index feature has been added! 2015.04.05 Happy Easter!!! 2015.04.04 Hope ya'll got a kick out of this years April Fools article (was there ever any doubt). All spoof articles are now archived in 2015.04.01 2015.03.30 Appendix D is added. 2015.03.27 A proof demonstrating E# to be of order-ω is published in the sub-article that can be seen here. The same paper may also be found in Appendix C. 2015.03.03 A massive upgrade to chapter 4.3 is finally complete. There are now 15610 ExE googolism's! Yes you read that right. 2015.01.01 Happy New Year!!! 2014.12.25 Merry Christmas!!! 2014.12.09 Today marks the 6th Anniversary of the Large Number Site! 2014.10.09 2014.09.23 Expanded version of Cascading-E article is completed. There is now 3263 googolism's below tethrathoth. 2014.09.09 Expanded version of Hyper-E article is completed. There are now 1220 E# and xE# numbers. 2014.05.21 My first googological paper can now be found in Appendix C. 2014.05.08 Upgrade to article xec_number2 with numbers and notation going way beyond a transmorgrifihgh! 2014.04.29 New article for Chapter 3.2 on the googology of Andre Joyce! 2014.04.20 Happy Easter! See brand new article here! 2014.01.30 2014.01.01 Happy New Year !!! 2013.12.09 Today marks the 5th Anniversary of The Large Number Site! |
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