Repeated Exponentiation
Just as exponentiation of natural numbers is motivated by repeated multiplication, it is possible to define an operation based on repeated exponentiation; this operation is sometimes called tetration. Iterating tetration leads to another operation, and so on. This sequence of operations is expressed by the Ackermann function and Knuth's up-arrow notation. Just as exponentiation grows faster than multiplication, which is faster growing than addition, tetration is faster growing than exponentiation. Evaluated at (3,3), the functions addition, multiplication, exponentiation, tetration yield 6, 9, 27, and 7,625,597,484,987 respectively.
Read more about this topic: Complex Numbers Exponential
Famous quotes containing the word repeated:
“Modern man likes to pretend that his thinking is wide-awake. But this wide-awake thinking has led us into the mazes of a nightmare in which the torture chambers are endlessly repeated in the mirrors of reason.”
—Octavio Paz (b. 1914)