# Number system

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*This article is not about numeral systems, which are systems of symbols for representing numbers.*

In mathematics, a **number system** is a set of numbers, or number-like objects, together with some arithmetic operations (e.g., addition and so on) that can be performed on them.

Examples of number systems are: natural numbers, integers, rational numbers, algebraic numbers, real numbers, complex numbers, p-adic numbers, surreal numbers, and hyperreal numbers.

As the phrase "number-like objects" is vague, so is the very concept of a number system. For example, whether the quaternions should be considered a number system is perhaps only a matter of convention. Rings of matrices are not usually considered number systems.