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
Famous quotes containing the words graham and/or number:
“Read the Bible. Work hard and honestly. And don’t complain.”
—Billy Graham (b. 1918)
“The Oregon [matter] and the annexation of Texas are now all- important to the security and future peace and prosperity of our union, and I hope there are a sufficient number of pure American democrats to carry into effect the annexation of Texas and [extension of] our laws over Oregon. No temporizing policy or all is lost.”
—Andrew Jackson (1767–1845)