What is bfn?

Big Fraction Notation (BFN)

Big Fraction Notation (BFN) is a non-standard, very expressive notation for representing extremely large numbers, often far beyond what can be expressed using standard scientific notation or even Knuth's up-arrow notation. It focuses on nested towers and iterated functions, making it powerful for describing fast-growing functions.

BFN is characterized by its layered structure and reliance on fundamental building blocks:

Base: The number being exponentiated, often a relatively small integer (e.g., 2, 10).
Height: The number of times the base is raised to a power.
Operation: The operation being repeated, often tetration, pentation, or beyond.
Layering: The use of multiple layers to represent extremely fast growth. Each layer describes how the previous layer grows.

Key features of BFN include:

Nested exponents: BFN uses towers of exponents, like base ^^ height, where ^^ represents tetration (repeated exponentiation).
Iteration of functions: The notation extends to iterating other hyperoperations like pentation, hexation, etc., represented by higher-order arrows.
Multiple Layers: It represents numbers as several layers of nested hyper operations. The topmost layers specify the repetition number for the next layer.

BFN has no universally agreed-upon formal definition, and variations exist. However, the underlying principle is to decompose extremely large numbers into manageable components of nested operations. It is commonly used in discussing and comparing the growth rates of functions in the context of large number theory and computational complexity.

Here are some important subjects associated with BFN:

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