: Unary is used to prove lower bounds. A problem that is intractable (NP-hard) with binary input may become trivially solvable with unary input because the input size explodes. This highlights the difference between strongly and weakly NP-complete problems.
Base 1 has no symbol for zero. Zero is the empty string. This works mathematically but is cumbersome in practice—how do you write an empty string in a fixed-width medium? base 1
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The Singularity of Representation: A Comprehensive Analysis of Base 1 (Unary) Systems : Unary is used to prove lower bounds
In the pantheon of numeral systems, Base 10 (decimal) reigns in everyday life, Base 2 (binary) powers the digital world, and Base 16 (hexadecimal) compresses machine code for human readability. Yet, lurking at the theoretical foundation of all counting lies the simplest, most ancient, and most paradoxical system: , the unary numeral system. Base 1 has no symbol for zero
In a universe of abstraction, Base 1 is the irreducible atom of quantity.
In the world of mathematics and computer science, we are accustomed to positional numeral systems like (decimal), Base 2 (binary), and Base 16 (hexadecimal). However, at the very beginning of the numerical spectrum lies Base 1 , also known as the Unary Numeral System .