Knuth’s up arrow notation
Knuth’s up arrow noation is a way of writing numbers which would be unwieldy in standard decimal notation. It expands on the exponential notation . Define and .
Obviously , so , but .
In general, , a tower of height .
Clearly, this process can be extended: and .
An alternate notation is to write for . ( times because then and .) Then in general we can define .
To get a sense of how quickly these numbers grow, is more than seven and a half trillion, and the numbers continue to grow much more than exponentially.
|Title||Knuth’s up arrow notation|
|Date of creation||2013-03-22 12:58:43|
|Last modified on||2013-03-22 12:58:43|
|Last modified by||Henry (455)|
|Synonym||up arrow notation|