# Numeral System

A Numeral System is a mathematical notation for representing numbers.

## References

### 2019

• (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Numeral_system Retrieved:2019-3-13.
• A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

The same sequence of symbols may represent different numbers in different numeral systems. For example, "11" represents the number eleven in the decimal numeral system (used in common life), the number three in the binary numeral system (used in computers), and the number two in the unary numeral system (e.g. used in tallying scores).

The number the numeral represents is called its value.

Ideally, a numeral system will:

• Represent a useful set of numbers (e.g. all integers, or rational numbers)
• Give every number represented a unique representation (or at least a standard representation)
• Reflect the algebraic and arithmetic structure of the numbers.
• For example, the usual decimal representation of whole numbers gives every nonzero whole number a unique representation as a finite sequence of digits, beginning with a non-zero digit. However, when decimal representation is used for the rational or real numbers, such numbers, in general, have an infinite number of representations, for example 2.31 can also be written as 2.310, 2.3100000, 2.309999999..., etc., all of which have the same meaning except for some scientific and other contexts where greater precision is implied by a larger number of figures shown.

Numeral systems are sometimes called number systems, but that name is ambiguous, as it could refer to different systems of numbers, such as the system of real numbers, the system of complex numbers, the system of p-adic numbers, etc. Such systems are, however, not the topic of this article.