Graham's Number
Graham's number itself can not be expressed accurately in Conway chained arrow notation, but by defining the intermediate function, we have: (see functional powers), and
Proof: Applying in order the definition, rule 3, and rule 4, we have:
- (with 64 's)
- (with 64 's)
- (with 64 's)
- (with 65 's)
- (computing as above).
Since f is strictly increasing,
which is the given inequality.
With chain arrows it is very easy to specify a much larger number. For example, note that
which is much greater than Graham's number.
Read more about this topic: Conway Chained Arrow Notation
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—Billy Graham (b. 1918)
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—George Gurdjieff (c. 1877–1949)