Talk:0.999.../Archive 9

message: This is not a problem with the article but with the wiki search engine. Searching for "1=0.999..." or "1 equals 0.999..." doesn't return anything usable. Could someone make a link from the inverted titles to this article so that "=" may become commutative again? Thx. 82.135.2.13 01:17, 10 August 2006 (UTC)
replies: text: Typing "Proof that 1 equals 0.999..." etc returns this article on the search though, but you need to use "proof". —Mets501 (talk) 01:28, 10 August 2006 (UTC)
thread_title: But what about 1=0.999...?

message: Well, I think "Order proof" and "Limit proof" are looking good. Next, that geometric series is getting lonely, so I'll be adding a complementary method in "Real analysis" using subdivided intervals, due to Bartle and Sherbert.
Then "Other number systems" could use more explicit ties to 0.999..., including a subsection on systems where "0.999..." doesn't mean 1: hackenstrings and Richman's "Cut D". Possibly the 10-adic expression ...999 could make an appearance somewhere. "Applications" could use a second application to justify the plural: perhaps the role of the converse in the decimal proof that the reals are uncountable? "In popular culture" needs a bit of expansion, and finally-- this is the hard part, but doable-- the introductions of the three major proof sections should start explaining their contexts: the desirability of theorems with weak hypotheses, and the diversity of pedagogical treatments of real numbers. Any takers for those tasks?
After all that, I'm thinking GA -> cook up some illustrations -> Peer Review -> FA -> Main Page -> peace and love.
In local news, I don't have a history book on hand. Can anyone fill in the details on the origin of the geometric series formula and its early proofs? Melchoir 18:39, 25 August 2006 (UTC)
thread_title:  Moving along... 

message: The new archive's date isn't a typo; I went from the absolute earliest post to the absolute latest post.  By a freak coincidence, someone replied to a two-month old discussion while I was moving the text, so I had to move that section back. Supadawg (talk • contribs) 20:51, 1 September 2006 (UTC)
thread_title:  Archive 08 

message: I've just made a trip through Google Book Search, and it appears that the treatment of 0.999… in real analysis textbooks is even more diverse than I thought. I'll be expanding the section, possibly adding a couple more subsections to clarify the differences; these will have the benefit that they will flow more naturally into the following section on rational numbers. One of them will take the sequence limit within the real numbers; I realize that we were trying to avoid such a limit and the associated infinity sign, but it's an important idea that gets referenced again and again. Also, some subsections will have to be renamed more precisely. Melchoir 18:22, 2 September 2006 (UTC)
thread_title:  Expanding "Real analysis" 

message: Add any additional comments
* Comment I didn't limit my explanation to one sentence, and I don't think we should.  Nor need we have a separate section for discussion. Michael Hardy 17:47, 5 September 2006 (UTC)
thread_title: Discussion

message: Apparently A. H. Lightstone, a student and coauthor of Robinson, addressed decimals in NSA not long after the field was created. Lightstone's POV, contrary to this article's suggestion, is that decimals in NSA are (1) easy and (2) a useful educational device:
:"The goal of this article is to enliven Abraham Robinson's concept of an infinitesimal by exhibiting infinitesimals in a simple and direct manner. ...To this end we shall exploit the familiar notion of the decimal expansion of a real number. After all, this notion improves our grasp of real numbers; just so, it will help us appreciate infinitesimals, indeed all numbers of our extended number system."
And that, kids, is why following references is better than doing original research. I was going to briefly expand on Hackenstrings next, but I think I'd better fix the overall readability first. Melchoir 17:10, 5 September 2006 (UTC)
thread_title:  Infinitesimals 

message: Hey, hang on, Supadawg. Wikipedia:Lead section advises us that the lead section should summarize the entire article. Shouldn't it? Melchoir 23:28, 5 September 2006 (UTC)
replies: text: Yes, it should summarize, but going into detail about how each proof is accomplished distracts the reader.  Wikipedia:Lead Section says the summary should be concise, and I interpret that as telling the reader what will be done, not how; that's for the body of the article.  The less fluff, the better. Supadawg (talk • contribs) 01:24, 6 September 2006 (UTC)
replies: text: Well, that's reasonable. I could go either way on the sentence listing the methods; they're an important part of the article but maybe the reader doesn't care so early on. If you feel strongly about it, okay. But what about the former third paragraph on skepticism, popular discussion, and alternate number systems? Melchoir 01:50, 6 September 2006 (UTC)

text: Oh, I see where you're going now. The lead will still need something, though... hmm. Melchoir 01:53, 6 September 2006 (UTC)

text: Possibly "the non-terminating decimal 0.999… (where the 9s recur)", or "the infinitely repeating decimal 0.999… (where the 9s recur)".  Or maybe the "(where the 9s recur)" part isn't necessary; it's obvious by the notation. Supadawg (talk • contribs) 02:46, 6 September 2006 (UTC)
replies: text: Yeah, I deleted it! So, you put it back by accident, then? Melchoir 03:01, 6 September 2006 (UTC)
replies: text: *checks edit history*  Yup, guess I did.  Sorry about that; re-removing it now. Supadawg (talk • contribs) 03:18, 6 September 2006 (UTC)
thread_title:  Lead section and popular culture