Difference between revisions of "Natural number"
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In [[mathematics]], a '''"natural" number''' is 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. | In [[mathematics]], a '''"natural" number''' is 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. | ||
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| + | It should be noted that natural numbers have not evolved over time, but have been woven into the fabric of the universe by God in their present state. | ||
==Axiomatization== | ==Axiomatization== | ||
Revision as of 01:24, April 24, 2009
In mathematics, a "natural" number is a number from the set {0,1,2,...}.[1] 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 integers and rational numbers.
It should be noted that natural numbers have not evolved over time, but have been woven into the fabric of the universe by God in their present state.
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 Axioms in his honor.
Reference
- ↑ 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." (Wolfram)