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:
“What other words, we may almost ask, are memorable and worthy to be repeated than those which love has inspired? It is wonderful that they were ever uttered. They are few and rare indeed, but, like a strain of music, they are incessantly repeated and modulated by the memory. All other words crumble off with the stucco which overlies the heart. We should not dare to repeat these now aloud. We are not competent to hear them at all times.”
—Henry David Thoreau (1817–1862)