**R function** is a googological function introduced by Wikia user Hyp cos in 2013^{[1]}. R function is often considered to be an extremely powerful googological notation, and may be on par with Strong array notation if both were properly defined. However, R function in its original form is unformalised, and thus cannot have a strength at all. Subsequently, Hyp cos released Version 2 and Version 2.0.1^{[2]}^{[3]} in an attempt to formalise the notation (Did he succeed?).

In 2020, an attempt to formalise the original R function was made by Wikia user 12AbBa (Zongshu Wu) in his web book^{[4]}. The definition is currently WIP.

At the core of R function is the operator "R", which is binary, left-associative, and operates on a positive integer (written to the left of "R") and an expression (written to the right of "R").

## Contents

## Terminology

12AbBa calls the positive integer before the "R" the **base**, and the positive integer after the "R" the **recursive part**^{[4]}. An **rsymbol** is a "symbol" that is allowed to appear in the recursive part. Note the rsymbols work differently than normal symbols, as "37" will be considered 2 symbols, but it is only 1 rsymbol.

## Basic R function

Basic R Function | |
---|---|

Type | Binary |

Based on | Exponentiation |

Growth rate | \(f_{\omega}(n)\) |

In Basic R function, there is only one type of rsymbol: a positive integer. As said above, a positive integer is considered one rsymbol. The recursive part is also only allowed to contain one rsymbol. Therefore, for any \(n\):

\(nR0=10^n\)

\(nR(k+1)=nRkRk\dots Rk\) w/\(n\) \("Rk"\)'s, if \(k\ge 0\)

### Examples

\(100R0=10^{100}=\) googol

\(100R1=100\underbrace{R0R0\dots R0}_{\text{100 R0's}}=\underbrace{10^{10^{⋰^{10^{100}}}}}_{\text{100 10's}}=\) grangol

\(100R2=100\underbrace{R1R1\dots R1}_{\text{100 R1's}}\approx\) greagol

\(100R3=100\underbrace{R2R2\dots R2}_{\text{100 R2's}}\approx\) gigangol

## Brace Notation

### Examples

## Linear Array Notation

### Examples

## Dimensional Array Notation

### Examples

## Nested Array Notation

### Examples

## Hyper Nested Array Notation

### Examples

## References

- ↑ https://googology.wikia.org/wiki/User:Hyp_cos/Basic_R_Function Basic R function
- ↑ https://googology.wikia.org/wiki/User_blog:Hyp_cos/R_function_II R function II
- ↑ https://googology.wikia.org/wiki/User_blog:Hyp_cos/R_function_v2.0.1 R function v2.0.1
- ↑
^{4.0}^{4.1}https://sites.google.com/view/extremelylargenumbers/chapter-1-fundamentals-of-large-numbers Fundamentals of Large Numbers (Chapter 1) - From One to Infinity and Beyond