Unary numeral system

The unary numeral system is the simplest numeral system to represent natural numbers:^[1] to represent a number N, a symbol representing 1 is repeated N times.^[2]

In the unary system, the number 0 (zero) is represented by the empty string, that is, the absence of a symbol. Numbers 1, 2, 3, 4, 5, 6, ... are represented in unary as 1, 11, 111, 1111, 11111, 111111, ...^[3]

Unary is a bijective numeral system. However, because the value of a digit does not depend on its position, it is not a form of positional notation, and it is unclear whether it would be appropriate to say that it has a base (or "radix") of 1, as it behaves differently from all other bases. ^{[citation needed]}

The use of tally marks in counting is an application of the unary numeral system. For example, using the tally mark | (𝍷), the number 3 is represented as |||. In East Asian cultures, the number 3 is represented as 三, a character drawn with three strokes.^[4] (One and two are represented similarly.) In China and Japan, the character 正, drawn with 5 strokes, is sometimes used to represent 5 as a tally.^[5][6]

Unary numbers should be distinguished from repunits, which are also written as sequences of ones but have their usual decimal numerical interpretation.