The Construction of Graham's Number

Article Summary

The primary goal of this article is to formally define and attempt to construct Graham's number. Explicit reference is made to the infamous googolplex and extensive use is made of the powerful Knuth up-arrow operators, which are a standardized notation for very large numbers, and are used to define Graham's number.

The primary goal of this article is to formally define and attempt to construct Graham's number, which appeared in the 1980 Guinness Book of World Records as being the largest number used in a formal mathematical proof.

To undertake this task, we first consider the representation of large numbers - in the sense of numbers that are of a significantly higher order than numbers used in everyday life, and to contrast these numbers against the magnitudes of very large physical astronomical quantities. Explicit reference is made to the infamous googolplex and extensive use is made of the powerful Knuth up-arrow operators, which are a standardized notation for very large numbers, and are used to define Graham's number.

You can read the full Graham's Number article by clicking here.
Article written by:
Ian Tame
Senior Tutor