Super-exponentiation

Super-exponentiation (also tetration or power-tower) is iterated exponentiation. It is often written using Knuth's up-arrow notation, hyper operators, Conway chained arrow, or as (a@b).

Using this final notation, we can create a recursive/inductive definition of super-exponentiation as a raised to the power a@(b-1), where a@1 is a.

Then the operation @ follows exponentiation in the sequence

Then, a@b:

each one inductively defined from the binary operation before.

Table of contents

1 Source
2 Some values
3 See also

Source

n@1 = n for all real numbers

n@0 = 1 for all real numbers

n@(-1) = 0 for all real numbers not equal to 1

n@(-2) = negative infinity for all real numbers greater than 1

n@(-2) = infinity for all real numbers between 0 and 1