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    What is the sum of the infinte series:

    1 - 1 + 1 - 1 + 1 - ...

    ?
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    (Original post by mikesgt2)
    What is the sum of the infinte series:

    1 - 1 + 1 - 1 + 1 - ...

    ?
    We can say that the sum is (1-1) + (1-1) + (1-1) + (1-1)...
    Which of course (1-1)=0, so it is like saying 0+0+0+0+0....
    which is 0.

    BUT, we can also say that 1 + (-1+1) + (-1+1) + (-1+1)....which means that it would be 1+ 0 +0 + 0 + 0 + 0 + 0...which is 1.

    Since both calculations give the same answer we can assume that 0 = 1.

    However why 2 different answers? Well since infinity has no defined value then the question itself is fallicious, so the answer you get is fallicious.
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    (Original post by 2776)
    We can say that the sum is (1-1) + (1-1) + (1-1) + (1-1)...
    Which of course (1-1)=0, so it is like saying 0+0+0+0+0....
    which is 0.

    BUT, we can also say that 1 + (-1+1) + (-1+1) + (-1+1)....which means that it would be 1+ 0 +0 + 0 + 0 + 0 + 0...which is 1.

    Since both calculations give the same answer we can assume that 0 = 1.

    However why 2 different answers? Well since infinity has no defined value then the question itself is fallicious, so the answer you get is fallicious.
    Anyone agree with me?
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    (Original post by 2776)
    Anyone agree with me?
    Yes. Spot on.
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    (Original post by 2776)
    Anyone agree with me?
    did you read that in the New Scientist issue about infinity?
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    (Original post by elpaw)
    did you read that in the New Scientist issue about infinity?
    I read the article today, about an hour ago.
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    (Original post by Ralfskini)
    I read the article today, about an hour ago.
    Is it in the latest issue?
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    (Original post by ditzy blonde)
    Is it in the latest issue?
    no it was from early october i think, cant remember exactly
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    (Original post by 2776)
    We can say that the sum is (1-1) + (1-1) + (1-1) + (1-1)...
    Which of course (1-1)=0, so it is like saying 0+0+0+0+0....
    which is 0.

    BUT, we can also say that 1 + (-1+1) + (-1+1) + (-1+1)....which means that it would be 1+ 0 +0 + 0 + 0 + 0 + 0...which is 1.

    Since both calculations give the same answer we can assume that 0 = 1.

    However why 2 different answers? Well since infinity has no defined value then the question itself is fallicious, so the answer you get is fallicious.
    Yup, I agree. But there is another possibility:

    Let the sum of the series be x

    We can say that: x = 1 - x
    => 2x = 1
    x = 1/2

    I think you could also argue that x = -1/2

    This was just an interesting thing I found in a book about infinity.
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    A baby could have worked that sum out! I don't know, Maths these days is getting easier and easier.
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    (Original post by elpaw)
    no it was from early october i think, cant remember exactly
    27th September. I'm a little behind.
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    (Original post by Ralfskini)
    27th September. I'm a little behind.
    your clock is running faster than mine. maybe i've been on some light speed travel lately.
 
 
 
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