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Bringing back 0.99999 = 1

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  • #1

    Bringing back 0.99999 = 1

    Sorry to bring this back guys. I have a question to ask.

    I know, I have heard all logic that 1 does equals 0.9999 forever if we see it as

    1=3/3
    3/3 divided by 3 = 1/3
    1/3=0.33333
    0.3333 x 3 = 0.99999

    Ok I know.

    But, if you put it on a graph, and make a ''timeline'', they never touch eachother. So, now I am undecided.

    Even a bit convinced that 1 does not equal 0.9999....

    If I am really off, explain to me why.

    Here comes the pwnage...

    Look at my quick drawing to be sure you guys understand me since I am so good at explaining my self in english .

    Spec.
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    -Never argue with an idiot; He will bring you down to his level and beat you with experience.
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  • #2
    The problem is that your graph describes a sequence [.9, .99, .999, .9999, ...], not a number (.9-repeating). A sequence can approach a number, e.g., the sequence [.9, .99, .999, .9999, ...] approaches 1 but never equals 1 (unless you do some shizznit with limits or whatever, but take this with a grain of salt, I'm a CS guy not a math guy, maybe limits don't apply to sequences, whatevah). However, a number doesn't approach anything -- it is fixed, static, [insert synonym for fixed/static]. The number .9-repeating does not "approach" anything -- it can be less-than, equal-to, or greater-than another number, but it cannot "approach" another number. Which is why your graph does not disprove ".9-repeating = 1."
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    • #3
      Dear Lord, not again.

      You have the vertical scale wrong. The difference between .9 and .99 is nine times larger than the difference from .99 to 1.

      Pick the smallest number greater than 0 that you can think of. I bet that I can find a point on the graph where the difference between one and the function you graphed is even smaller.

      Alternatively, take a calculus class and pay attention when they talk about series convergence.
      "Beware of the man who works hard to learn something, learns it, and finds himself no wiser than before. He is full of murderous resentment of people who are ignorant without having come by their ignorance the hard way. "
      -Bokonon

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      • #4
        Loin, how can 0.999 repeating be fixed if we dont know where it ends?

        Spec.
        -Never argue with an idiot; He will bring you down to his level and beat you with experience.

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        • #5
          Because it doesn't end.
          "Beware of the man who works hard to learn something, learns it, and finds himself no wiser than before. He is full of murderous resentment of people who are ignorant without having come by their ignorance the hard way. "
          -Bokonon

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          • #6
            So its not fixed then....sort of....But its not 1

            Unless you see it as 1.00000 repeating, which would never end either. But it will always be one.

            So 0.99999 repeating will never be fixed.

            Spec.
            -Never argue with an idiot; He will bring you down to his level and beat you with experience.

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            • #7
              CRIKEY! This, again!
              Life is not measured by the number of breaths you take, but by the moments that take your breath away.
              "Hating America is something best left to Mobius. He is an expert Yank hater.
              He also hates Texans and Australians, he does diversify." ~ Braindead

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              • #8
                And also, if 0.9999 repeating = 1

                then,

                What does 0.333 repeating equal to? 0.34, 0.334, 0.3334....

                This may sound simple for some of you. But sorry, I would really like to understand.

                Thanks.

                Spec.
                -Never argue with an idiot; He will bring you down to his level and beat you with experience.

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                • #9
                  Originally posted by SlowwHand
                  CRIKEY! This, again!
                  Yes!



                  Spec.
                  -Never argue with an idiot; He will bring you down to his level and beat you with experience.

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                  • #10
                    Originally posted by Spec
                    So its not fixed then....sort of....But its not 1
                    Numbers do not change. The number 2 is greater than the number 1 today, and it's going to be greater than the number 1 tomorrow. The number .9-repeating doesn't equal ".9-repeating carried out to fifty decimal places" today and ".9-repeating carried out to fifty-one decimal places" tomorrow -- the number is fixed, static, [insert synonym for fixed/static here]. The number .9-repeating equals 1 today, and it will equal 1 tomorrow.

                    Originally posted by Spec
                    What does 0.333 repeating equal to?
                    1/3
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                    • #11
                      Originally posted by loinburger
                      The number .9-repeating equals 1 today, and it will equal 1 tomorrow.
                      Why isn't it 1 then?

                      Spec.
                      -Never argue with an idiot; He will bring you down to his level and beat you with experience.

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                      • #12
                        Originally posted by loinburger

                        1/3
                        Ohhh!! I understand.

                        0.9999999 is a fraction like 3/3 because it would be wrong to call it 1.



                        Spec.
                        -Never argue with an idiot; He will bring you down to his level and beat you with experience.

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                        • #13
                          Originally posted by Spec
                          Why isn't it 1 then?
                          For the same reason that 2/2 isn't 1? I'm not sure I understand the question.
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                          • #14
                            So its not fixed then....sort of....But its not 1
                            No, it's fixed. The addition of 9*10^(-n) gets smaller and smaller as n increases. That infinite sum adds up to 1. The reason why is that regardless of how small a positive number you pick, at some point another addition of a 9*10^(-n) will make the difference between the sum and 1 even smaller. Again, please read a book on calculus for elucidation.
                            "Beware of the man who works hard to learn something, learns it, and finds himself no wiser than before. He is full of murderous resentment of people who are ignorant without having come by their ignorance the hard way. "
                            -Bokonon

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                            • #15
                              Originally posted by Spec
                              0.9999999 is a fraction like 3/3 because it would be wrong to call it 1.
                              You seem to be arguing that it's wrong to have two (or more) equivalent representations of the same quanitity.

                              "I have fifty cents."
                              "WHY DON'T YOU JUST SAY YOU HAVE HALF A DOLLAR YOU STUPID JERK???"

                              Half a dollar = fifty cents = some unspecified number of rupees. .9-repeating = 3/3 = 1.
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