Chris Bird has done a lot of work on large numbers, including much original work that goes beyond that of others. He has created a system of fast-growing recursive functions that rivals or exceeds the functions of Jonathan Bowers and others.
Of the following files, the first describes the relationship between his linear arrays (the first and slowest-growing of his recursive functions) and the well-known Conway chained arrow notation. The numbered chapters are a series describing Bird's functions and notation step by step. The Fast-Growing Hierarchy in Terms of Bird’s Array Notations, as the title indicates, correlates Bird's work with the Fast-growing hierarchy and the Veblen hierarchy, and also to a few other well-known notations and functions such as Conway arrows, Friedman, Goodstein, etc. (the other documents also have some references to these functions).
These versions were written in 2012, with substantial updates to the later chapters in 2013; much of the material is similar to earlier work by Chris Bird going back to 2006 or earlier. He lives in England, and holds a Master's degree in mathematics despite suffering from Asperger's Syndrome (a form of autism).
Chris Bird's Super Huge Numbers
Proof that Bird's Linear Array Notation with 5 or more entries goes beyond Conway's Chained Arrow Notation.
1. Linear Array Notation (last updated 1 Apr 2012)
2. Multi-Dimensional Array Notation (last updated 2 Apr 2012)
3. Hyper-Dimensional Array Notation (last updated 2 Apr 2012)
4. Nested Array Notation (last updated 2 Apr 2012)
5. Beyond Nested Arrays I (last updated 7 May 2013)
6. Beyond Nested Arrays II (last updated 5 May 2013)
7. Beyond Nested Arrays III (last updated 31 Mar 2012)
8. Beyond Nested Arrays IV (NEW – finished 27 May 2013)
The Fast-Growing Hierarchy in Terms of Bird’s Array Notations (last updated 24 May 2013)
Bowers' Named Numbers
This is an auxiliary document listing many of the "named" big numbers of Jonathan Bowers, and giving values of these in terms of Bird's notation.
Bowers' Named Numbers (last updated 19 Mar 2012)
These files are written by and are copyright © 2006-2013 Chris Bird.
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