A numeral system is a writing system

Writing system

A writing system is a symbolic system used to represent elements or statements expressible in language.-General properties:Writing systems are distinguished from other possible symbolic communication systems in that the reader must usually understand something of the associated spoken language to...

 for expressing numbers, that is a mathematical notation

Mathematical notation

Mathematical notation is a system of symbolic representations of mathematical objects and ideas. Mathematical notations are used in mathematics, the physical sciences, engineering, and economics...

 for representing number

Number

A number is a mathematical object used to count and measure. In mathematics, the definition of number has been extended over the years to include such numbers as zero, negative numbers, rational numbers, irrational numbers, and complex numbers....

s of a given set, using graphemes or symbols in a consistent manner.
It can be seen as the context that allows the symbols "11" to be interpreted as the binary

Binary numeral system

The binary numeral system, or base-2 number system, represents numeric values using two symbols, 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2...

 symbol for three, the decimal

Decimal

The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....

 symbol for eleven, or a symbol for other numbers in different bases

Radix

In mathematical numeral systems, the base or radix for the simplest case is the number of unique digits, including zero, that a positional numeral system uses to represent numbers. For example, for the decimal system the radix is ten, because it uses the ten digits from 0 through 9.In any numeral...

.

Ideally, a numeral system will:

• Represent a useful set of numbers (e.g.