0.999... = 1

Discussion in 'Physics & Math' started by Andrej64, Jun 8, 2006.

  1. Klippymitch Thinker Registered Senior Member

    Messages:
    699
    Yeah your correct.

    and for absane.

    You cant just jump to infinite. Numbers follow a sequence of 123456789 you cant jump or skip through the sequence only with logical thought processes can this happen. For when we give objects numbers. 3 red mm's + 2 red mm's = 5 red mm's
     
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  3. Absane Rocket Surgeon Valued Senior Member

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    8,989
    When am I "jumping to infinite?"

    As for the rest of what you said.... I don't see the connection between that and everything I said.
     
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  5. Klippymitch Thinker Registered Senior Member

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    699
    I can't see how you can't see the connection.
     
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  7. Absane Rocket Surgeon Valued Senior Member

    Messages:
    8,989
    Well I understand what you mean. For example we have number \(x_{0}x_{1}...x_{n}\) in base ten such that \(x_{0},x_{1},...,x_{n} \in \{0, 1, 2, ..., 8, 9\}\)

    But what's the connection? Fill in the blanks... I can't read minds over the Internet.
     
  8. Sciencelovah Registered Senior Member

    Messages:
    4,349
    Err.. that, and as you have been said somewhere else, 0.999... is equal to 1.
    So is that mean 1 - 0.9999... = 0 or 0.0000.....

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    I suppose you will say 0, because there is no number between 0 and 0.0000...

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    Sorrrrry if that irritates you, I'm not a mathematician, yet I have a bit interest in it.
     
  9. Sciencelovah Registered Senior Member

    Messages:
    4,349
    and btw,.. when we want to sum up a number which contain 9 behind a decimal to get a result which contain 0 as in:

    0.9
    0.1
    --- +
    1.0

    or

    0.1009
    0.0001
    ---------+
    0.1010

    arent we always have to add this with something contain 1?
    So, shouldnt it be: 1 - 0.9999..... = 0.00000...........1 ?

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    then which one is equal to 0? 0.0000.... or 0.00000.....1 ?

    p.s: ok, ok I'll read from 1st page, maybe will find something there. I was expecting a volunteer to give a summary for that

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    Last edited: Oct 12, 2007
  10. przyk squishy Valued Senior Member

    Messages:
    3,151
    Oh it's perfectly simple really. 1 = 123456789, so 0 = 123456788 and 0 = 1. This in turn implies that all reals are equal to each other. There are no bigger or smaller numbers. All numbers are equally big and small. I think this is in line with draqon's philosophies.
     
  11. Absane Rocket Surgeon Valued Senior Member

    Messages:
    8,989
    Yes.

    0 = 0.000...

    You'll only start to irritate me if you are arrogant enough to think you know more about mathematics

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  12. Nasor Valued Senior Member

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    6,221
    "0.000...1" is self-contradictory. The "..." means that the zeros repeat forever. If they repeat forever, there's no way for there to be a 1 on the end.
     
  13. Absane Rocket Surgeon Valued Senior Member

    Messages:
    8,989
    Ahh.. she made a correction. Thanks.
     
  14. Sciencelovah Registered Senior Member

    Messages:
    4,349
    Thanks, too, from me.

    Ok I understand now that this number is exist:
    0.9999999............ which is equal to 1


    so I assume that:

    0.8888888............ is equal to 0.89

    and 0.898888...... is equal to 0.899

    So the result of:
    0.89888....... - 0.8888....... = 0.899 - 0.89 = 0.009

    Is it correct?? It is strange for me because how can you substract something
    unlimited by another unlimited thing and then get a limited thing

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  15. przyk squishy Valued Senior Member

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    3,151
    No. The general "rule" goes something like this: if you have an infinite sequence of 9's in the decimal representation of a number, you can remove it and increase the next digit to the left by 1. For example:

    0.8899999...​

    There's an infinite sequence of 9's after the 8, so you can remove it and add 1 to the 8. So:

    0.8899999... = 0.89

    It also works inside a sequence of 9's:

    0.99999999...​

    If we try to add 1 to the 9, it becomes 10 and we have to carry the 1 to the next digit on the left. This goes on until we run out of 9's

    This only works for repeating 9's. Other sequences of repeating digits can be expressed as fractions, eg:

    \(0.888 \ldots = \frac{8}{9}\)​
     
  16. Sciencelovah Registered Senior Member

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    4,349
    Ok, thanks, but that has not answer my question yet... or

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  17. przyk squishy Valued Senior Member

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    3,151
    Well 0.89888... - 0.88888... = 0.01, if that's what you wanted to know. The rules you learned in primary school for adding and subtracting numbers digit-by-digit still apply.
     
  18. Sciencelovah Registered Senior Member

    Messages:
    4,349
    Is it not 0.009? Surely 0.009 is not equal to 0.01


     
  19. Absane Rocket Surgeon Valued Senior Member

    Messages:
    8,989
    0.00999... = 0.01.

    As P said, all your normal rules of addition and subtraction work. The difficulty you are having is trying to deal with addition and subtracting with an infinite number of digits. As far as I understand, no one truly knows how to subtract decimal numbers with an infinite number of digits (assuming you don't rewrite it into another forum or make assumptions). Of course, many assumptions are reasonable like with: 0.333... - 0.123123123... = 0.210210210... because the pattern appears to repeat. But if you have sqrt(2) - sqrt(3) = 1.41421356... - 1.73205081... = ? How do we do this? Clearly, we can't start from the very "right hand side" because there is no right hand side. Starting from the left hand side and we have to keep making corrections when caring numbers over to towards the right (what I mean is if we have 73-68... we can see 7-6 = 1 and 3 - 8 = -5. But, we can't have -5 in the answer so we take "10" from "1" and make that 0 and add 10 to -5. The answer is 5.)


    Sorry if I confused you.
     
  20. D H Some other guy Valued Senior Member

    Messages:
    2,257
    Both of these are wrong. (Others have said the same but not explicitly). Everything that follows hinges on these mistakes.

    The correct interpretation is 0.898... - 0.888... = 0.01.

    As both numbers involve repeating decimal fractions they are both rational numbers. You may have taught how to convert these to rationals: 9*0.89888... = 10*0.898888... - 0.898888... = 8.9888... - 0.898888... = 8.09. Thus 0.89888... = 8.09/9 = 809/900. Similarly, 0.888... = 8/9. Subtracting, 809/900-8/9 = 9/900 = 1/100 = 0.01.

    Why is this confusing? 1/3 + 1/6 = 0.333... + 0.166... = 0.499... = 0.5 = 1/2.
     

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