Talk:Natural number

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linking to 19th century[edit]

I've reworded the phrase that includes "19th century". I believe it should be linked. Objections?174.3.125.23 (talk) 23:58, 4 March 2015 (UTC)

My intuition is that it should probably not be linked. I don't think a passage on mathematical developments in the 19th century is a terribly natural place for a reader to say, "oh, that reminds me, I want to find out more about the 19th century in general".
Anyway, that's just my impression, since you asked. If you feel like linking 19th century, I'm not going to revert you. Others may feel differently. --Trovatore (talk) 05:10, 5 March 2015 (UTC)
Ideally, to improve such a powerful crosslinkable encyclopedia, proper nouns should be linked. I'll go ahead and link the century.174.3.125.23 (talk) 02:41, 6 March 2015 (UTC)
Oh, no, sorry, that's completely the wrong criterion. See WP:OVERLINKING. Absolutely no way all proper nouns should be linked. Link only when there's a reasonable probability a typical reader would want to follow the link.
I promised not to revert you so I won't, but I invite you to undo this edit after reading the guidance I linked to. (Europe should not be linked either, and the two links right next to each other are especially problematic, because it looks like a single link to 19th century Europe.) --Trovatore (talk) 04:14, 6 March 2015 (UTC)

ClueBot NG hides ID[edit]

I do not critisize the revert which has been done by the bot on the article page in removing the word "incorrectly", but I consider judging this to be beyond a bot's capability.

I wanted to have this checked and tried to get to the required ID but failed. This ID is truncated, possibly because of the lenght of an IPv6 address. I could not deal with the variant "on my talk page" and also looking for the edits of ClueBot NG did not make this ID available to me.

I apologize if I abused this page by posting this kind of trouble here. Please, let me know where it were appropriate, in case. Purgy (talk) 08:55, 5 March 2015 (UTC)

I agree. It seems like a purposed use of hiding someone's ip address with such a blatant contradiction of the definition.174.3.125.23 (talk) 02:44, 6 March 2015 (UTC)
Yes the revert seems good, being done by a bot does not. Paul August 14:09, 6 March 2015 (UTC)

paragraph removed[edit]

I have removed the paragraph

The attempt by Frege[clarification needed] mentioned above, as modified by Russell, where each natural number n is defined as the set of all sets with n elements has been modified to avoid paradoxes.[1][2] This definition at first may appear circular, but can be made rigorous with care. Define 0 as {{ }} (clearly the set of all sets with zero elements) and define S(A) (for any set A) as {x ∪ {y} | xAyx} (see set-builder notation). Then 0 will be the set of all sets with zero elements, 1 = S(0) will be the set of all sets with one element, 2 = S(1) will be the set of all sets with two elements, and so forth. The set of all natural numbers can be defined as the intersection of all sets containing 0 as an element and closed under S (that is, if the set contains an element n, it also contains S(n)). One could also define "finite" independently of the notion of "natural number", and then define natural numbers as equivalence classes of finite sets under the equivalence relation of equipollence. To avoid the paradoxes that occur in the usual systems of axiomatic set theory (because the collections (classes) involved are too large), we need to drop the axiom of separation); the resulting variant of set theory is called New Foundations. There are other attempts to reformulate set theory without the axiom of separation, and these variants have been shown to be consistent if New Foundations is consistent. Another approach is found in some systems of type theory.
  1. ^ Die Grundlagen der Arithmetik: eine logisch-mathematische Untersuchung über den Begriff der Zahl (1884). Breslau.
  2. ^ Whitehead, Alfred North, and Bertrand Russell. Principia Mathematica, 3 vols, Cambridge University Press, 1910, 1912, and 1913. Second edition, 1925 (Vol. 1), 1927 (Vols 2, 3). Abridged as Principia Mathematica to *56, Cambridge University Press, 1962.

In fact, except for the first sentence, it is not sourced. It mention the "set" {x ∪ {y} | xAyx} and talk about the "set of all sets with one element", which are clearly not sets, by Russel's paradox (does {S(0)} belongs to S(0)?). It asserts without sourcing that there are set theories such as New Foundations that may solve these paradoxes, but does not mention that the text of the paragraph is wrong in the most used set theory named ZF. Thus it is unsourced, mathematically wrong and does not have a neutral point of view. Therefore I have removed it. D.Lazard (talk) 21:09, 6 March 2015 (UTC)

For clarification's sake, ===Modern definitions=== does mention Frege, but probably in a historical context, not a mathematical context.174.3.125.23 (talk) 22:12, 6 March 2015 (UTC)

For the record that paragraph was added here by Randall Holmes (talk · contribs). Paul August 22:51, 6 March 2015 (UTC)

Debated sentences.[edit]

Purgy Purgatorio wants the following sentences in the lead and reverted my deletion of it. "This distinction is of no fundamental concern for the natural numbers as such, since their core construction is the unary operation successor. Including the number 0 just supplies an identity element for the (binary) operation of addition, which makes up together with the multiplication the usual arithmetic in the natural numbers, to be completed within the integers and the rational numbers, only." Please explain what "to be completed within the integers and the rational numbers, only," means.Rick Norwood (talk) 17:49, 4 July 2015 (UTC)

This last clause is intended to refer to the arithmetic, which cannot be completed within the naturals but requires the mentioned extensions. May I cordially invite you to find a more suitable formulation in elegance and succinctness?
It is important to me to state, that I did not revert anything, but reformulated a deleted content, putting an aggravated distinction in a more reasonable perspective, to conform to mentioned deficiencies. Purgy (talk) 15:36, 3 July 2015 (UTC)

Sorry for my error. I now understand your reformulation. Rick Norwood (talk) 12:58, 4 July 2015 (UTC)

No problem! My invitation is still sustained to find a better formulation for the intended fact. I'm not perfectly satisfied myself, but also not sufficiently eloquent in this. Purgy (talk) 17:23, 4 July 2015 (UTC)

"count from zero"[edit]

In the latest version [1], "count from zero" was removed. I understand it was rewritten to include the "historical" context behind the convention of including zero. Just thought I'd bring it up to explain that the link could be piped to include the deeper topic of including zero for "computer programmers".96.52.0.249 (talk) 10:51, 4 July 2015 (UTC)

Does my last linking the job for you in sufficient manner? Honestly, I did not expect an article on this, even if it misses the true origin. I'll look after it. Purgy (talk) 17:17, 4 July 2015 (UTC)