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0.99~=1

Discussion in 'Mathematics and Physics' started by rumiam, Apr 17, 2007.

  1. arod

    arod New Member

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    0.33... = 1/3. You are trying to quantify infinity in your definition.
     
  2. dknguyen

    dknguyen Well-Known Member

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    0.999...~= 1? Yes!
    0.999... = 1? No.

    End of story. If you do write down 1 in your calculations, it's because the difference is so small it doesn't matter (same reason why we round numbers).
     
    Last edited: Apr 19, 2007
  3. Pommie

    Pommie Well-Known Member Most Helpful Member

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    The result is e (2.71828). Try setting infinity to 1 then 10, 100, 1000, 10,000 etc. The graph levels out at e.

    Mike.
     
  4. dave

    Dave New Member

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  5. ljcox

    ljcox Well-Known Member

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    I did not say that 0.33... = 1/3. I said it approaches 1/3 as the number of decimal places approaches infinity.

    No, I'm not trying to quantify infinity, I'm simply stating a mathmetical fact.

    You can't quantify infinity, you can only approach it.
     
  6. ljcox

    ljcox Well-Known Member

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    If you read the original question it was "0.99 -continuious- = 1" and the answer is no. Rounding up is a different issue.
     
  7. ljcox

    ljcox Well-Known Member

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    You can't divide by infinity or raise a number to the power of infinity.

    If x = 1/n then x approaches 0 as n approaches infinity.

    If x = 1^n then x =1 for all n. But n = ∞ is not valid. n can only approach ∞.
     
  8. Pommie

    Pommie Well-Known Member Most Helpful Member

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    And, as X approaches infinity then (1+1/X)^X approaches e.

    Mike.
     
  9. arod

    arod New Member

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    0.33~ = 1/3 => That is mathematical fact. What could it possibly be "approaching?" Here is one of many proofs:

    c = 0.999~
    10c = 9.999~
    10c - c = 9.9999~ - 0.999~
    9c = 9
    c = 1

    Hard to argue with that. Whether you want to believe it or not, this is accepted by all mathematicians. If you still don't want to believe me, I will show you the convergence of the infinite geometric series when I get home later today.
     
  10. gramo

    gramo New Member

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    umm, where did e come from? :eek:
     
  11. Pommie

    Pommie Well-Known Member Most Helpful Member

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    The natural constant e is the amount in billions of dollars that google was valued at when it floated on the NYSE. It is also the base of natural logarithms. See wiki.

    In fact they define e as,
    [​IMG]

    Mike.
     
  12. dknguyen

    dknguyen Well-Known Member

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    0.999 fixed to 0.999...
     
  13. ljcox

    ljcox Well-Known Member

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    Correct me if I'm wrong, but I don't see how you can subtract 2 numbers that have an infinite number of decimal places. To do a subtraction, you start at the last digit. eg. 7.89 - 3.45, you start with 9 - 5.

    But with an infinite number of decimal places, there is no last digit.

    I will be interested to see your convergence of an infinite geometric series.
     
  14. Optikon

    Optikon New Member

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    It is not hard to argue with because it is not mathematically correct. :D

    Your first & last statement say that C = 0.999~ and also that C =1 implying that 1 = 0.999~ which is NOT true.

    It is true however that Lim (n->inf) {0.999~} = 1 where n is number of repeating 9's. So your statements as they stand are NOT correct and the convergence of the geometric series is not the issue here technically. The geometric series convergence depends on the existence of its limit. You are showing no limits which is why it is wrong.
     
  15. rumiam

    rumiam New Member

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    ok if 1 does not = 0.99999~ then explain to me;
    why is it that
    1/3 = 0.333~
    2/3 = 0.666~
    3/3 = 0.999~

    3/3= 1
    so
    1= 0.999~

    Prove this to be wrong
     
  16. ljcox

    ljcox Well-Known Member

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    Your error is in adding the decimal values for 1/3 and 2/3

    These have an infinite number of decimal places and so I don't see how you can add them.
     
  17. ljcox

    ljcox Well-Known Member

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    I was intrigued by this so I did the maths to prove it. See attachment. What I forgot to write is that the first 3 terms in the last line are the first in the infinite series for e. The terms after 1/n go to 0 as n approaches infinity.
     

    Attached Files:

    Last edited: Apr 20, 2007
  18. ljcox

    ljcox Well-Known Member

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    I think the answer to this issue is in whether the attached series converges to 1 or to 0.9999~.

    It is many years since I studied maths that I don't recall how to do the test for convergence of this series and don't have the time to revise it.

    So if any knows how to do it, please enlighten us.
     

    Attached Files:

  19. Sceadwian

    Sceadwian Banned

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    I don't believe this post is still going.
     
  20. arod

    arod New Member

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    Yes, isnt that the point of the proof? Showing that .999~ = 1...
    I don't think you understand. When I type 0.999~, it means that the 9s repeat to infinity.

    Instead of me reinvinting the wheel, here is a page showing the convergence of an infinite geometric series proving that 0.999~ = 1
     
  21. tkbits

    tkbits Member

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    How about an alternate proof?

    Code (text):
        0.9999....
       -----------
    9 ) 9.0000....
        8 1
        ---
          90
          81
          --
           90
           81
           --
            90
            81
            --
             9....
     
     

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