Natural number - Revision history

DavidB4-bot: clean up & uniformity

2016-07-13T16:30:08Z

clean up & uniformity

RSchlafly: 0 is a natural number. there is no dispute.

2013-02-23T18:35:48Z

0 is a natural number. there is no dispute.

Ed Poor: including 0

2013-02-22T14:05:18Z

including 0

Ed Poor: dispute matters to grade-school students who want high grades

2013-02-22T13:58:24Z

dispute matters to grade-school students who want high grades

Ed Poor: The grade-school math textbook I'm using specifically excludes zero

2013-02-22T13:55:10Z

The grade-school math textbook I'm using specifically excludes zero

RSchlafly: trend to include zero in his 1919 book

2010-07-19T18:41:41Z

trend to include zero in his 1919 book

Chippeterson: Undo revision 655993 by Godlymath (Talk)

2009-04-24T01:34:35Z

Undo revision 655993 by Godlymath (Talk)

Godlymath at 01:24, April 24, 2009

2009-04-24T01:24:59Z

Foxtrot: grammar, link

2009-02-16T12:21:11Z

grammar, link

Mathgeek123 at 22:38, December 25, 2008

2008-12-25T22:38:47Z

@@ Line 1: / Line 1: @@
-In [[mathematics]], a '''"natural" number''' is a number from the set {0,1,2,3,...}.<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. [[Bertrand Russell]] remarked on the trend to include zero in his 1919 book.[http://jeff560.tripod.com/n.html] 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.
+In [[mathematics]], a '''"natural" number''' is a number from the set {0,1,2,3,...}.<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. [[Bertrand Russell]] remarked on the trend to include zero in his 1919 book.[http://jeff560.tripod.com/n.html] 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.
 ==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==
 <references/>
 [[Category:Mathematics]]

@@ Line 1: / Line 1: @@
-In [[mathematics]], a '''"natural" number''' is a number from the set {1,2,3,...}.<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. [[Bertrand Russell]] remarked on the trend to include zero in his 1919 book.[http://jeff560.tripod.com/n.html] 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 {0,1,2,3,...}.<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. [[Bertrand Russell]] remarked on the trend to include zero in his 1919 book.[http://jeff560.tripod.com/n.html] 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.
 ==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==

@@ Line 6: / Line 6: @@
 ==Disputes==
 Some math textbooks, particularly on the college level, include zero. Most elementary school textbooks distinguish between the ''[[whole number]]''s (i.e., non-negative [[integer]]s 0,1,2,...) and the ''[[counting number]]''s (i.e., positive integers 1,2,3,...) - defining natural numbers as identical to counting numbers.
 Students need to check the definition used in their textbook to avoid having test questions marked "wrong".

@@ Line 3: / Line 3: @@
 ==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]]

← Older revision		Revision as of 13:55, February 22, 2013
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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. [[Bertrand Russell]] remarked on the trend to include zero in his 1919 book.[http://jeff560.tripod.com/n.html] 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 {1,2,3,...}.<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. [[Bertrand Russell]] remarked on the trend to include zero in his 1919 book.[http://jeff560.tripod.com/n.html] 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==		==Axiomatization==

← Older revision		Revision as of 18:41, July 19, 2010
Line 1:		Line 1:
−	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. [[Bertrand Russell]] remarked on the trend to include zero in his 1919 book.[http://jeff560.tripod.com/n.html] 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==		==Axiomatization==

← Older revision		Revision as of 01:34, April 24, 2009
Line 1:		Line 1:
	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.
−
−	~~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==

← Older revision		Revision as of 01:24, April 24, 2009
Line 1:		Line 1:
	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.
		+
		+	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==

← Older revision		Revision as of 12:21, February 16, 2009
Line 1:		Line 1:
−	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.	+	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.

	==Axiomatization==		==Axiomatization==

← Older revision		Revision as of 22:38, December 25, 2008
Line 1:		Line 1:
−	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.	+	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==		==Axiomatization==