Unary numeral system

A numeral system that represents a nonnegative integer by repeating one tally mark, with the number of marks equal to the represented value.

Tally marks: Counting marks used to record quantities, often grouped in sets of five. Unary numerals extend tallying into a positional-free written notation.
Natural number: A number used for counting or ordering, with conventions about whether zero is included. Unary most directly represents natural-number quantities through their mark counts.
Peano axioms: An axiomatic foundation for the natural numbers based on zero and the successor operation. Repeated unary marks mirror building each natural number by successive increments.
Roman numerals: A numeral system using letters and subtractive or additive combinations to represent numbers. Roman numerals also use repeated symbols, but combine several symbol values and rules.
Unary encoding: A coding scheme that represents an integer using a number of identical symbols proportional to its value. It formalizes unary numerals as a representation used in computing and information theory.
Zero: The integer that denotes no quantity and serves as the additive identity. Unary needs an empty string or a special convention to represent zero.
Unary coding: A variable-length code that represents a nonnegative integer by a run of identical bits, often terminated by a delimiter. It adapts unary’s run length to encode integers in digital communication.
Decimal numeral system: A positional numeral system using ten digits, with each place representing a power of ten. Decimal notation represents large numbers with far fewer symbols than unary.
Unary addition: Addition performed by concatenating the symbol sequences representing the two operands. Combining mark strings directly gives the unary representation of their sum.
Positional notation: A numeral system in which a digit’s value depends on its position. Unary assigns value by symbol count, not by digit position or place value.

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