Talk:Natural number

New page

I just completely removed the WP import and started from scratch. Peter Schmitt 11:47, 19 August 2009 (UTC)

Good idea. :) One thing: Because of their importance every civilization has developed a numeral system for representing and manipulating natural numbers, both in oral and written language.... I think the use of "civilization" is problematic and should be changed to "technologically developed cultures have...", something like that. Finally, I would note the interesting and controversial research by Dan Everett on the Pirahã people and language. He claims there are no fixed words for numbers, which could have implications for the way they manipulate quantities cognitively. Cognition is one reference. Most of this is rather controversial in linguistics. John Stephenson 11:58, 19 August 2009 (UTC)

This is a very interesting pointer! However, I think that the concept and history of numbers and numerals deserve and should have articles of their own. The present article should concentrate on the basics of (today's) understanding and use of natural numbers. As for "civilization": Isn't "technologically developed" too restrictive? Would you agree with "culture" (alone)? Peter Schmitt 12:17, 19 August 2009 (UTC)

Related Articles - What to include?

What should -- and what should not -- be included into the related articles list?

I ask this because of recent changes and additions by Daniel with which I do not agree. And, may be, MiltonHoward does not approve my changes to his list. These different opinions are probably caused by different interpretations of the purpose of the related articles list. (It can be assumed that no one claims the list is already complete.)

This question should probably be discussed at a general place - it is not special to this page. But it is easier to use a specific topic as example.

My view is that the related articles should provide suggestions for further reading. That means that the listed articles can be recommended to readers whose main interest is the topic of the page. That can be both more and less links than those embedded in the text.

Here are the three list. I shall comment below.

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Howard's first entries: Parent topics

• Number theory [r]: The study of integers and relations between them. ^[e]
• Set theory [r]: Mathematical theory that models collections of (mathematical) objects and studies their properties. ^[e]
• Computer science [r]: The study of how computers work, and the algorithms, data structures and design principles used in their operation and programming. ^[e]
• Mathematical logic [r]: Add brief definition or description

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my changes: Parent topics

• Number [r]: One of the fundamental concepts of mathematics, used for such purposes as counting, ordering, and measuring. ^[e]

Subtopics

• Numeral system [r]: Add brief definition or description
• Peano axioms [r]: A set of axioms that completely describes the natural numbers. ^[e]
• Elementary arithmetic [r]: Add brief definition or description

Other related topics:

• Cardinal number [r]: The generalization of natural numbers (as means to count the elements of a set) to infinite sets. ^[e]
• Number theory [r]: The study of integers and relations between them. ^[e]
• Computer science [r]: The study of how computers work, and the algorithms, data structures and design principles used in their operation and programming. ^[e]

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Daniel's changes: Parent topics

• Mathematics [r]: The study of quantities, structures, their relations, and changes thereof. ^[e]
• Number theory [r]: The study of integers and relations between them. ^[e]
• Number [r]: One of the fundamental concepts of mathematics, used for such purposes as counting, ordering, and measuring. ^[e]

Subtopics

• Numeral system [r]: Add brief definition or description
• Peano axioms [r]: A set of axioms that completely describes the natural numbers. ^[e]eeeeeeeeee
• Elementary arithmetic [r]: Add brief definition or description

Other related topicsee

• Cardinal number [r]: The generalization of natural numbers (as means to count the elements of a set) to infinite sets. ^[e]
• Complex number [r]: Numbers of the form a+bi, where a and b are real numbers and i denotes a number satisfying $i^{2}=-1$. ^[e]
• Computer science [r]: The study of how computers work, and the algorithms, data structures and design principles used in their operation and programming. ^[e]
• Abacus [r]: A mechanical aid to performing arithmetic which dates back many centuries and is still used in modern times. ^[e]
• Finger [r]: Add brief definition or description

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That Computer Science and Mathematical Logic both have to do with natural numbers is, in my opinion, not enough to make them "parent topics", and I do not think that they are "related" either: You will not learn about natural numbers if you consult them. (I left CS as related, nevertheless, but with doubts.) I hesitated to put Set Theory to related because I do not see how this could help the reader (a link from the text is sufficient). I moved Number Theory to related because -- while (elementary) NT certainly deals with N -- it does not "include" their foundation -- it uses them.

Daniel added Mathematics as parent. I would say it is a great great great parent. It does not help to put it on the list of every mathematics article. (Would you expect "Earth" for every geography article on some town?) (And he moved back NT).
His additions to related: Complex number - well, why not integer, rational, real, as well? I thought of number system or something, but was not yet sure about the best title. Abacus? This is - one of many - topics from (maybe) (history of) elementary arithmetic, or similar. It will be related to Numeral System. But here? And Finger? Because you can calculate with fingers?

Is my view of Related Articles mistaken? Or are my arguments wrong? What would a potential reader looking for information say? Peter Schmitt 00:40, 20 August 2009 (UTC)

Let me say my thinking was somewhat reversed -- it was less that a reader would learn more about natural numbers by going to computer science, as a computer science reader would get confirmation that natural numbers are relevant to their searching. Other than a deplorable and incoherent explanation in junior high school when the "new math" was popular, I first encountered a serious discussion of natural numbers in my Discrete Mathematical Structures in Computer Science course and books. The explanations in those sources generally present them after set theory, but many graduates tend to link those two areas as related. Howard C. Berkowitz 15:40, 27 August 2009 (UTC)

Peter, you mentioned my name above: "And, maybe, Milton does not approve my changes to his list". Exactly what are you referring to? I have never had any contact with this article before to the best of my memory. Milton Beychok 15:59, 27 August 2009 (UTC)

I posted my reply at the forum to facilitate discussion. Milt, I guess Peter referred to a hypothetical situation. --Daniel Mietchen 16:11, 27 August 2009 (UTC)

Milton, I used your name by mistake. I corrected it in one place but overlooked the second mention. Sorry, I apologize. Peter Schmitt 16:14, 27 August 2009 (UTC)