\begin{definition}[Definition:Positional Numeral System]
A '''positional number system''' is a number system with the following properties:
:It has a set of numerals which represent a subset of the numbers.
:The number being represented is written as a string of these numerals, which represent a different value according to their position in the numerals.
The design of the '''positional number system''' is such that all numbers can be represented by such a string, which may or may not be infinite in length.
\end{definition}