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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").

## 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
TypeBinary
Based onExponentiation
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

## References

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