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ADA.org: Oral Health Topics: Tooth Numbering Systems ada.org | Health Care System, Phone Numbers... stmarysathens.com | System :: Quick Reference Phone Numbers... wrh.org | Health System - Frequently Called Numbers monhealth.com |
This article is about different sets of numbers. For different methods of expressing numbers with symbols, see numeral system. In mathematics, a 'number system' is a set of numbers, (in the broadest sense of the word), together with one or more operations, such as addition or multiplication. Examples of number systems include: natural numbers, integers, rational numbers, algebraic numbers, real numbers, complex numbers, p-adic numbers, surreal numbers, and hyperreal numbers. For a history of number systems, see number. For a history of the symbols used to represent numbers, see numeral system.
[edit] Logical construction of number systems[edit] Natural numbersMain article: Set-theoretic definition of natural numbers Simply put, the natural numbers consist of the set of all whole numbers greater than zero. The set is denoted with a bold face capital N or with the special symbol Giuseppe Peano developed axioms for the natural numbers, and is considered the founder of axiomatic number theory. [edit] More advanced number systemsThe word number has no generally agreed upon mathematical meaning, nor does the word number system. Instead, we have many examples. Thus there is no rule to say what is a number and what is not. Some of the more interesting examples of abstractions that can be considered numbers include the quaternions, the octonions, the sedenions, the trigintaduonions, ordinal numbers, and the transfinite numbers. [edit] See also[edit] Notes
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. (In some books, the natural numbers begin with 0. There is no general agreement on this subject.)
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