While it might seem like a mathematical curiosity, Base 1 is the simplest way to represent numbers and has deep roots in human history and logic. What is Base 1?
Unary coding is a specific entropy encoding used in data compression. It represents a positive integer $n$ as $n$ ones followed by a zero (or $n$ zeros followed by a one). base 1
Thus, the representation of a natural number ( n ) in Base 1 is a sequence of ( n ) identical symbols: While it might seem like a mathematical curiosity,
: Unary numbers (e.g., Peano numerals S(S(0)) ) are the natural representation for inductive proofs. It represents a positive integer $n$ as $n$
Arithmetic in Base 1 is algorithmically trivial but computationally expensive.
You have likely used Base 1 without realizing it. The most common application is . Whether a scorekeeper is marking points on a chalkboard or a prisoner is scratching lines on a cell wall in a movie, they are using Base 1. Advantages of Tallying in Base 1: