Super-logarithm
Arithmetic function / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Super-logarithm?
Summarize this article for a 10 year old
In mathematics, the super-logarithm is one of the two inverse functions of tetration. Just as exponentiation has two inverse functions, roots and logarithms, tetration has two inverse functions, super-roots and super-logarithms. There are several ways of interpreting super-logarithms:
- As the Abel function of exponential functions,
- As the inverse function of tetration with respect to the height,
- As a generalization of Robert Munafo's large number class system,
This article needs additional citations for verification. (November 2007) |
For positive integer values, the super-logarithm with base-e is equivalent to the number of times a logarithm must be iterated to get to (the Iterated logarithm). However, this is not true for negative values and so cannot be considered a full definition. The precise definition of the super-logarithm depends on a precise definition of non-integer tetration (that is, for not an integer). There is no clear consensus on the definition of non-integer tetration and so there is likewise no clear consensus on the super-logarithm for non-integer inputs.