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Number systems include the familiar integers, rationals, reals, etc. as well as unusual extensions of these sets such as p-adic and hyperreal numbers.

### Contents of this section:  Number Systems Introduction Integers Gaussian Integers Algebraic Integer Eisenstein Integer Quaternion Integers Quadratic Field Real Number Complex Number Algebraic Number Hypercomplex Algebras Quaternion Octonion Sedenion Matrix P-adic Hyperreal Surreal

### Internet references

Wikipedia: Number system

### Related pages in this website

Set Theory - description notation, terminology (e.g. Cartesian product, power set, cardinality) and construction of sets

The Peano Postulates -- Proving the properties of natural numbers using the Peano Postulates, which have been formulated so that zero is not included in the set of natural numbers.  (There's quite a debate about this point.)

Introduction to Counting -- explains what mathematicians mean by "counting" -- that is, putting sets in one-to-one correspondence.

Construction -- Construction of sets of numbers, starting with the original Peano Axioms, formulated so that zero is included in the set of natural numbers. (See Is Zero a Natural Number?)

The webmaster and author of this Math Help site is Graeme McRae.