Tetration

Tetration is the hyperoperation which comes after exponentiation. ${\displaystyle ^{x}{y}}$ means y exponentiated by itself, (x-1) times. List of first 4 natural number hyperoperations, the inverse of tetration is the super root shown in the example

1. Addition

   ${\displaystyle a+n=a+\underbrace {1+1+\cdots +1} _{n}}$

   n copies of 1 added to a.

2. Multiplication

   ${\displaystyle a\times n=\underbrace {a+a+\cdots +a} _{n}}$

   n copies of a combined by addition.

3. Exponentiation

   ${\displaystyle a^{n}=\underbrace {a\times a\times \cdots \times a} _{n}}$

   n copies of a combined by multiplication.

4. Tetration

   ${\displaystyle {^{n}a}=\underbrace {a^{a^{\cdot ^{\cdot ^{a}}}}} _{n}}$

n copies of a combined by exponentiation, right-to-left.

The above example is read as "the nth tetration of a".