A number system is a set of objects on which arithmetic operations can be performed.

Examples of number systems are: the real numbers, the rational numbers, the algebraic numbers, the complex numbers, the p-adic numbers, the surreal numbers, the hyperreal numbers. Whether, for example, the quaternions should be considered to comprise a number system is perhaps only a matter of convention.

This is not to be confused with the concept of a numeral system, a system of symbols for representing numbers.