Rational number

2009-10-18T16:41:09Z

Mathgeek123:

A '''"rational" number''' is a quotient of the form <math>\frac{a}{b}</math> where ''a'', ''b'' are [[integer]]s and ''b'' ≠ 0. The set of rational numbers, usually denoted by <math>\mathbb{Q}</math> is an example of a [[totally disconnected set]] that is not [[locally compact]]. The rational numbers are [[countable]]. Rational numbers can be identified by their fractional form, or a terminating or repeating decimal.

[[Category: Mathematics]]

Natural number

2008-12-25T22:38:47Z

Mathgeek123:

In [[mathematics]], a '''"natural" number''' is a a number from the set {0,1,2,...}.<ref>0 is usually included in the list of natural numbers in modern textbooks (Bourbaki 1968, Halmos 1974). + Older books sometimes exclude [[zero]], as there is a long history of people thinking that zero is unnatural or not really a number. Ribenboim (1996) states "Let P be a set of natural numbers; whenever convenient, it may be assumed that 0 in P." [http://mathworld.wolfram.com/NaturalNumber.html (Wolfram)] </ref> Natural numbers were used initially for counting ("there are three cows in this field"), but they took on the purpose of ordering as well ("She is the 2nd fastest person alive). These are specific instances of the more general notions of [[cardinality]] and [[ordinality]] which slowly become more complicated as one treats [[infinite]] numbers as well. The set of natural numbers is [[countable]]- via [[bijection]], this property can be used to prove the countability of the [[integer]]s and [[rational number]]s.

==Axiomatization==
In the late 19th century, [[Giuseppe Peano]] (August 27, 1858 – April 20, 1932) elaborated ''the'' axiomatic system for the Natural Numbers, later named [[Peano's Axioms|Peano Axioms]] in his honor.
==Reference==
<references/>

[[Category:Mathematics]]

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Rational number

Natural number