Talk:0.999.../Arguments/Archive 2

message: Copy Summarized from normal talk By E-Bod
Also for those of use that use "0.999 repeating" as a physical representation of an abstract number "approaching but not equal to" one we need a new variable.  Has a new variable been given (No pun in tended).
For instant although .999¯ equals one ... when we graph the number line (-∞,1),(1,∞) or (x≠1) How do we illustrate the "conceptual number" before and after 1 or any other whole number.  Before we proved this we just used .999¯ and .000¯1 to say this concept.  Now that we Proved this number actually does not exist we need a new way of saying what we have to say.  This Proof is hard to Grasp because we don't have an alternative to illustrate the idea.  
Remember that "1" is a symbol for a number. And if ".999¯" equals one then it is just a #REDIRECT 1.  We now need a new Title for XYZ.--E-Bod 22:38, 11 June 2006 (UTC)
replies: text: That's the point of the proof: The number that "approaches 1 but isn't" does not exist (at least, not in the standard reals we usually employ). As to the significance, I can't think of any "real world applications" right now. This proof should just show the non-existence of such an "approaching number" and thus clarify our mental image of the reals. . Yours, Huon 09:04, 12 June 2006 (UTC)
replies: text: Ok I accept that The number that "approaches 1 but isn't" does not exist.  In that Definition of exist it seems really Obvious.  That's not a Tangible Number.  However If Approaching but not Equal to Does not Exist then ∞ Does not Exist Eather.  Lets say you make a tan graph :Image:Tangent.svg There is a the Concept of the Last point you gen go to Approaching  π/2 And still be in The Domain of the Function. We have represented this as π/2)(π/2 or ≠ π/2.  As a Teaching tool we could say for a similar graph That went to infinity at alone as we can't have one but we can have .9 .99 .999 .9999 etc or 1.1 1.01 1.001 1.0001 1.00001.  Just like the Final number does not Exist in the Real world we still  have imaginary numbers with real life applications (I think rocket science or something).  I know that in some Online games it is possible to get 2 points connect with a 0 distance rope.  Ideal gasses (Which don't exist) take up 0 Volume at 0K (Kelvin).  Even if the number does not exist that does not mean we can't still represent the non existing number.  If somebody Does Find the replacement other than .9999Bar then we are laking something in this article.  Or in Math Knowledge in General.  Just remember No Original Research--E-Bod 00:07, 13 June 2006 (UTC)
replies: text: First, I don't think you have given a concrete example where usage of .999¯, 0.000¯1 or the like really helps in any way; 0 did just fine for the ideal gas example (though if one also dicusses negative temperatures, the symbol +0 can be used to emphasize that this is the positive zero). Even if such an example is provided, I'm not sure it is within the scope of the article, as it is about a mathematical concept, where such vague explanations have no place. This doesn't mean that there isn't a mathematical way to address the ideas you describe - Just that they aren't really related to what the article is about. -- Meni Rosenfeld (talk) 15:45, 13 June 2006 (UTC)
replies: text: The number you ask for exists, but it isn't in the reals. See infinitessimals. What you want is 1 - dx. Now, as stated before, could you name a single use for it? Or is this just to give you mental closure? -- He Who Is[ Talk ] 19:21, 19 June 2006 (UTC)
thread_title:  The number that "approaches 1 but isn't" does not exist 

message: Aren't the algebraic proofs easily refutable?  0.333...*3 has never equaled 0.999... according to my knowledge of simple algebra.  That would be an incorrect multiplication of repetends, and go against the multiplicative property.  Likewise with 10*0.999...=9.999... —Preceding unsigned comment added by 207.118.6.122 (talk • contribs) 
:No, it's correct.  How exactly does is the multiplication of repetends incorrect?  In 0.333...*3, 3 is multiplied by each digit in 0.333..., or 1/3, yielding the infinite series 0.999..., or 1.  The same goes for 10*0.999..., which equals 10. Supadawg (talk • contribs) 01:21, 2 September 2006 (UTC)
replies: text: What is 0.333...+0.333...+0.333... then? Melchoir 01:36, 2 September 2006 (UTC)

text: Yes, they add up to 1, but they also add up to 0.999....  This is because 0.999... equals 1.  Please explain how they do not add up that way, because you can proceed in adding them up the same way as with multiplication:  .3 + .3 + .3 = .9, .03 + .03 + .03 = .09, into infinity.  And please sign your comments, using four tildes (~~~~) so we can keep track of who said what. Supadawg (talk • contribs) 01:48, 2 September 2006 (UTC)
thread_title:  Incorrect use of Algebra?