Draft:Outline of numbers

The following outline is provided as an overview of and topical guide to numbers:

A number is a mathematical object used to count, measure, and label. The most basic examples are the natural numbers: 1, 2, 3, 4, 5, and so forth. Individual numbers can be represented in language with number words or by dedicated symbols called numerals; for example, "five" is a number word and "5" is the corresponding numeral. As only a limited list of symbols can be memorized, a numeral system is used to represent any number in an organized way. The most common representation is the Hindu–Arabic numeral system, which can display any non-negative integer using a combination of ten symbols, called numerical digits. Numerals can be used for counting (as with cardinal number of a collection or set), labels (as with telephone numbers), for ordering (as with serial numbers), and for codes (as with ISBNs). In common usage, a numeral is not clearly distinguished from the number that it represents.

What type of things are numbers?

Numbers can be described as all of the following:

• Abstract concepts
  • Symbols (Numeral system)
    • Fundamental elements of mathematics
      • Quantitative descriptors

Types of numbers

Main article: List of types of numbers

Natural numbers

Main article: Natural numbers

• Supernatural numbers

• Extended natural numbers

Integers

Main article: Integers

• Even and odd numbers
• Prime numbers
• Composite numbers

• Polygonal numbers
• Quadratic integers
• Profinite integers

Real numbers

Main article: Real numbers

• Positive numbers
• Negative numbers
• Rational numbers
• Irrational numbers
  • Quadratic irrational numbers

• Definable real numbers
  • Constructible numbers
  • Computable numbers
• Normal numbers
• Fuzzy numbers
• Liouville numbers
• Extended real numbers

Complex numbers

Main article: Complex numbers

• Imaginary numbers
• Algebraic numbers
  • Algebraic integers
    • Salem numbers
  • Perron numbers

• Periods
• Gaussian integers
  • Gaussian rationals
• Eisenstein integers
• Extended complex numbers

Hypercomplex numbers

Main article: Hypercomplex numbers

• Split-complex numbers
• Bicomplex numbers
• Multicomplex numbers
• Dual numbers
  • Dual quaternions

• Quaternions
  • Split-quaternions
  • Biquaternions
    • Split-biquaternions
  • Hyperbolic quaternions

• Octonions
  • Split-octonions
  • Bioctonions
• Sedenions
• Trigintaduonions

Other types

• Surreal numbers
• Superreal numbers
• Hyperreal numbers

• Cardinal numbers
• Ordinal numbers
• Transfinite numbers
• p-adic numbers

History of numbers

Main article: History of numbers

• History of ancient numeral systems
• History of natural numbers
  • History of prime numbers
• History of integers
  • History of 0
• History of real numbers
  • History of negative numbers
  • History of irrational numbers
    • History of pi
• History of complex numbers
• History of infinity

Applications of numbers

• Accounting

• Calculation

• Counting

• Mathematics

General numbers concepts

• Numeral system