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Math Help - What's wrong with this proof...

  1. #1
    jtl
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    What's wrong with this proof...

    Hello there. What's wrong with this proof:

    1/3=0.3333333333...
    3/1=3

    (1/3)*(3/1)=(1*3/3*1)=(3/3)=1

    and

    (1/3)+(1/3)+(1/3)=0.3333333..+0.3333..+0.33333..=3*(1/3)=0.999999999999999

    So 0.9999999999...=1
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by jtl View Post
    Hello there. What's wrong with this proof:

    1/3=0.3333333333...
    3/1=3

    (1/3)*(3/1)=(1*3/3*1)=(3/3)=1

    and

    (1/3)+(1/3)+(1/3)=0.3333333..+0.3333..+0.33333..=3*(1/3)=0.999999999999999

    So 0.9999999999...=1
    I really think you're allowed to round 0,9999999999999999999999999 off to 1.
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  3. #3
    jtl
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    Quote Originally Posted by janvdl View Post
    I really think you're allowed to round 0,9999999999999999999999999 off to 1.
    Yeah, but doesn't the proof above say 0.99999999999999999999... is equivalent to 1?

    I'm a bit confused here.
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  4. #4
    Bar0n janvdl's Avatar
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    Quote Originally Posted by jtl View Post
    Yeah, but doesn't the proof above say 0.99999999999999999999... is equivalent to 1?

    I'm a bit confused here.
    No, most definitely not.

    Look at this:

    0,9 - close to 1
    0,99 - even closer
    0,999 - closer!

    You get the idea.

    See 1/3 = 0,3333333...
    Those 3's never stop. They go on into infinity.

    So what does that mean?
    0,99999... is always tending to become 1. It will get so close to 1, that we could just as well right 1.

    Do you understand?
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  5. #5
    jtl
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    Quote Originally Posted by janvdl View Post
    No, most definitely not.

    Look at this:

    0,9 - close to 1
    0,99 - even closer
    0,999 - closer!

    You get the idea.

    See 1/3 = 0,3333333...
    Those 3's never stop. They go on into infinity.

    So what does that mean?
    0,99999... is always tending to become 1. It will get so close to 1, that we could just as well right 1.

    Do you understand?
    So if the 3's in 0.3333.... never stop, then shouldn't it be infinity?
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  6. #6
    Bar0n janvdl's Avatar
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    Quote Originally Posted by jtl View Post
    So if the 3's in 0.3333.... never stop, then shouldn't it be infinity?
    No.

    The 3's only keep repeating. Infinity is different.

    Don't try to make things harder. Keep it simple.

    0,99999999 is always getting closer and closer to 1. It will later be so close that we could just as well write 1.
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  7. #7
    jtl
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    First of all thanks janvdl. And yes I know you can round it off. This isn't homework or anything to do with school. I just wrote that proof, and I'm wee bit bewildered.

    My question is regarding the proof, whether it's wrong or not. That's what's confusing me.

    Thanks again for your replies.
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  8. #8
    Bar0n janvdl's Avatar
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    Quote Originally Posted by jtl View Post
    First of all thanks janvdl. And yes I know you can round it off.

    My question is regarding the proof, whether it's wrong or not. That's what's confusing me.
    Can you give me the actual question please?

    I can see nothing wrong with using either 0,333... or  \frac{1}{3} , its the same thing.
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  9. #9
    jtl
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    Quote Originally Posted by janvdl View Post
    Can you give me the actual question please?
    There's no question. That's the proof, i'm asking whether there is something wrong with it.
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  10. #10
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    Quote Originally Posted by jtl View Post
    I just wrote that proof, and I'm wee bit bewildered.
    My question is regarding the proof, whether it's wrong or not. That's what's confusing me.
    Please tell us about yourself. What is the level of your understanding about geometric series? The answer to your questions actually turns on infinite geometric series.
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  11. #11
    Bar0n janvdl's Avatar
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    Quote Originally Posted by jtl View Post
    There's no question. That's the proof, i'm asking whether there is something wrong with it.
    No, as far as i know, there is nothing wrong with using either 0,3333... or  \frac{1}{3} , because they are the same thing, so i would say no, there isn't anything wrong with the proof, not on my level or your level of mathematics anyway.


    This can get kind of complicated, im thinking of hyperbolas. 0,9999... is always nearing to 1, but never actually becomes 1...
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  12. #12
    jtl
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    Quote Originally Posted by Plato View Post
    Please tell us about yourself. What is the level of your understanding about geometric series? The answer to your questions actually turns on infinite geometric series.
    I finished my A'Levels (basically highschool) and took a gap year before uni. My mathematical knowledge has been drained because of the gap year, I need to start learning again.

    My level of knowledge on Geometric Series is well nothing cause I don't remember much.

    Any ways, if this involves geometric series, it would be real helpful if you could give me some points or links to get this.

    Thanks.
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  13. #13
    Bar0n janvdl's Avatar
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    Quote Originally Posted by jtl View Post
    I finished my A'Levels (basically highschool) and took a gap year before uni. My mathematical knowledge has been drained because of the gap year, I need to start learning again.

    My level of knowledge on Geometric Series is well nothing cause I don't remember much.

    Any ways, if this involves geometric series, it would be real helpful if you could give me some points or links to get this.

    Thanks.
    I am not sure how to apply this to a geometric series, so it would be better if Plato takes over from here.
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  14. #14
    jtl
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    Quote Originally Posted by janvdl View Post
    I am not sure how to apply this to a geometric series, so it would be better if Plato takes over from here.
    No problem. Thanks anyway.

    Oh and plato, so is the proof wrong?
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  15. #15
    Grand Panjandrum
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    Quote Originally Posted by jtl View Post
    Hello there. What's wrong with this proof:

    1/3=0.3333333333...
    3/1=3

    (1/3)*(3/1)=(1*3/3*1)=(3/3)=1

    and

    (1/3)+(1/3)+(1/3)=0.3333333..+0.3333..+0.33333..=3*(1/3)=0.999999999999999

    So 0.9999999999...=1
    The result you "prove" is correct but you are using processes that you do
    not justify. In particular how do you know that:

    0.333..+0.333..+0.333..= 0.999..

    what method have you used to add the things on the left of this
    equation?

    RonL
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