Hyperoperation

A hyperoperation is a generalization of addition, multiplication, exponentiation, tetration, etc. They are often written using Knuth's up-arrow notation. Natural number level hyperoperations can be defined recursively as a piecewise function:

$H_n(a,b)=\{\begin{array}{cc}b+1& \text{if }n=0\\ a& \text{if }n=1,b=0\\ 0& \text{if }n=2,b=0\\ 1& \text{if }n\ge 3,b=0\\ H_{n-1}(a,H_n(a,b-1))& \text{otherwise}\end{array}$

Template:Math-stubThis is used to express really large numbers while being able to write them.