Talk:0.999.../Archive 1

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Please add new archivals to Talk:Proof that 0.999... equals 1/Archive02. (See Wikipedia:How to archive a talk page.) Thank you. Rasmus (talk) 13:37, 16 November 2005 (UTC)
thread_title: Untitled

message: Consider the following proof that I propose be substituted for the one in this article: assume first that 0.999... and 1 are distinct. Between any two distinct real numbers lies another real number (infinitely many, in fact). Since there is no real number between 0.999... and 1, we have reached a contradiction and our original assumption must be false. Therefore, 0.999... and 1 are not distinct (i.e. they are equal in value). Q.E.D.. Shutranm 01:27, 7 May 2005 (UTC)
replies: text: Using the proofs in this article, your question can be reduced to 2/2.  This is 1. silsor 21:20, 7 November 2005 (UTC)

text: Well, you've convinced me! silsor 03:59, 10 November 2005 (UTC)
thread_title:  Keep in mind your knowledge of mathematics 

message: I created Proof that 0.999... equals 1/Alternate proofs to help keep the main page brief, but also allow us to post as many proofs as we'd like. --BradBeattie 15:39, 8 May 2005 (UTC)
replies: text: Subpages aren't allowed in the main article namespace (see Wikipedia:Subpages), you can put it on a different page, but I'd just put them on the main page, I think. People don't have to scroll down if they don't want to. Maybe we could create a suppage of this talk page and put all the proofs there while discussing which should be included. --Mike C | talk 16:13, 8 May 2005 (UTC)
thread_title: Subpages

message: I think the page needs a section on common misconceptions and flaws in the reasoning of these misconceptions. If the abracadabra section on the talk page says anything, it's that some people don't really get this. BradBeattie
: But the new section should probably be not too long. (The set of all common misconceptions of people is by several orders of magnitude larger than the set of all knowledge. :) Oleg Alexandrov 22:24, 6 May 2005 (UTC)
replies: text:  I very much agree. Maybe something as short as the top 3 misconceptions. No doubt our anonymous friend here is providing us with detail. The links I found these arguments taking place on should also provide a starting point. I'll look through later on and try to put a short summary together. --BradBeattie 22:30, 6 May 2005 (UTC)
replies: text:  I think this is fruitless. If you define the recurring decimal as a limit, and believe in geometric series, you are done. WP should consist of true facts; but doesn't in general need to convince people of themm if they insist on being wrong. There is no alternate POV to be represented. Other pages that are just magnets for discussion threads have in the end been dealt with in a similar way. Charles Matthews 18:01, 8 May 2005 (UTC)
thread_title:  New section: Arguments against 

message: I think this page should just be merged into recurring decimal. Charles Matthews 16:17, 8 May 2005 (UTC)
thread_title:  Merger with [[recurring decimal]] 

message: Your "proof" lies on two notions. First there is that \infty + 1 = \infty . You can you say XXX... =\infty  But Your second notion \frac{\infty}{\infty}=1 is totally nonsense. -Santa Claus 21:02 At Northpole Time.
:That is nonsense: There is no mention of ∞/∞ in this article. Michael Hardy 21:22, 8 May 2005 (UTC)
thread_title:  infinity divided by infinity 

message: Today I reverted some new content added to this article by anonimous user 130.230.47.130. My comment was "reverted ignorant contribution". I must say that I was wrong, actually that is meaningful text. But looks kind of long. Would anybody take a look at that contribution  and see if anything can be included in the article? Thanks. Oleg Alexandrov 18:47, 13 Jun 2005 (UTC)
thread_title:  My reversal 

message: Unlike all the items listed in that article, this one has valid proofs. Not appropriate there. Oleg Alexandrov 16:24, 23 July 2005 (UTC)
replies: text: I disagree as well. I'm reverting the change. --BradBeattie 13:58, 24 July 2005 (UTC)
thread_title:  Disagree with merging to [[invalid proof]] 

message: What's the point of having the -9 and 9? I find it demeaning, superfluous, and do to my overly analytical nature, confusing. The summation converges to 1 on it's own, why bother with adding the 9? Unless of course you're trying to make a parallel to the dumbed down version, which is neither necessary or has been noted. --24.126.30.46 03:50, 16 October 2005 (UTC)
replies: text: The 9 and -9 are put in so that you have the 9 x sum etc. bit, which is neccesary for the proof. Mallocks 20:30, 17 October 2005 (UTC)
replies: text:  Not convinced. Removed the -9. --Tob 15:29, 20 October 2005 (UTC)
thread_title:  Do Not Feed The Troll (and a comment) 

message: As I see it, there is no fault or handwaving in the 10x - x proof. It all depends on what machinery you have available. When writing things such as 0.333\dots, most people assume the existence of some set of reals and then define 0.333\dots as the limit of 0.3,\, 0.33,\, 0.333,\, \dots in that given set of reals. But then elementary calculus tells you that multiples and sums of converging sequences are again converging and the obvious rules, i.e.  2 \cdot 0.333\dots = 0.666\dots  apply. 
After taking everything into account which necessarily has to be known or accepted to be able to 'ask' the question whether 0.999\dots = 1, a useful proof from my point of view is 
1 = 3 \cdot \frac{1}{3} = 3 \cdot 0.333\dots = 0.999\dots,
since most readers probably believe the lemma 
\frac{1}{3} = 0.333\dots,
and those who actually know how to prove it can easily see how to modify that proof for one to the original question.
Of course this is biased since I am speaking from personal experience; this is how I convinced myself at the age where I asked that question for the first time. 
I object to the 'Property of real numbers' proof, though. It is correct that there are infinitely many real numbers between any given two distinct ones. But why is there no number between 0.999\dots and 1? 
--Tob 15:29, 20 October 2005 (UTC)
replies: text: Could you please provide proof that shows the two are not equal? I'd think that if all experts on the matter agree that they do, that the burden is on you to provide solid evidence against their equality. --BradBeattie 13:09, 25 October 2005 (UTC)

text: But, as was previously pointed out in this discussion, numbers only look like approximations in certain bases. I think we'd both agree that pi is irrational in base 10, but pi is represented as 10 in base pi and is therefore an integer in that base. Semantics aside, all of these symbols we use comprise the language of mathematics. They represent the idea of a number. The symbols 1/2, 0.5, 0.1 in base 2, 0.4999... represent the same value. It's important not to confuse the denotation with the connotation. --BradBeattie 15:55, 25 October 2005 (UTC)
replies: text: Please.  There is no such thing as "irrational in base 10" as opposed to irrational in some other base.  An irrational number is simply one that cannot be written as a ratio of two integers.  Bases have nothing to do with the definition. Michael Hardy 21:08, 25 October 2005 (UTC)

text: Actually, you can have bases of complex (or at least irrational) numbers. Take for example phinary. --24.126.30.46 07:36, 27 October 2005 (UTC)
thread_title:  10x - x