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:
“Lift not thy spear against the Muses’ bower:
The great Emathian conqueror bid spare
The house of Pindarus, when temple and tower
Went to the ground; and the repeated air
Of sad Electra’s poet had the power
To save the Athenian walls from ruin bare.”
—John Milton (1608–1674)