So the sum of all natural numbers from 1 to infinity is...

Discussion in 'Community Discussion' started by AustinIllini, Jan 20, 2014.

  1. AustinIllini, Jan 20, 2014
    Last edited: Jan 20, 2014

    AustinIllini macrumors demi-god

    AustinIllini

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    #1
  2. chabig macrumors 68040

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    #2
    The thread title is wrong. They are not summing the real numbers. They are summing the natural numbers (or positive integers) but NOT the real numbers.
     
  3. AustinIllini thread starter macrumors demi-god

    AustinIllini

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    #3
    Crap, you're right.
     
  4. chabig macrumors 68040

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  5. AustinIllini thread starter macrumors demi-god

    AustinIllini

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    #5
    Thanks!
     
  6. chabig macrumors 68040

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    #6
    That's a great article. I read it yesterday and watched the video...fascinating and completely non-intuitive. Not only does the sum turn out to be small, but it's negative despite all the components being positive. Thanks for sharing it here.
     
  7. mobilehaathi macrumors G3

    mobilehaathi

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    #7
    This is not quite the summation I think most of you are thinking about.
     
  8. Tomorrow macrumors 604

    Tomorrow

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  9. chabig macrumors 68040

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    #9
  10. localoid macrumors 68020

    localoid

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    #10
    Isn't this "Ramanujan summation"?

    [​IMG]

    If so, then this Web page offers some insight into this sort of "brain melting maths"...

     
  11. vrDrew macrumors 65816

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    #11
    I think a lot of the problem most of us normal people have is that we always mentally stop the process at some point short of infinity. And so we inevitably, mentally, come up with an unbelievably massive number.

    But true infinity (which by definition, we can never reach) yields a quite different result.

    Thought experiments like this always serve to remind me that there is a whole world out there, where "common sense" yields results that are strikingly at odds with the actual results.

    Always useful to keep in mind.
     
  12. Mousse macrumors 68000

    Mousse

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    #12
    Dagnabbit. These mathematicians are messing with the fabric of reality again. One of these days, someone is gonna divide by zero and then...:rolleyes:
     
  13. plinden macrumors 68040

    plinden

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    #13
    It's been a long time since I've done any math like this, but I feel a bit queasy watching the video. I may have been able to understand 20 years ago, but I can no longer really explain why - manipulating the infinite series in this way just doesn't feel right, if only because the explanation doesn't take into account anything that's happening at infinity.

    In fact, you can easily show 0 = 1 by similarly rearranging infinite series.
     
  14. AustinIllini thread starter macrumors demi-god

    AustinIllini

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    #14
    There may have been flaws in the demonstration (I don't believe so), but the applications of the summation in physics provides some validity in my mind.
     
  15. AustinIllini thread starter macrumors demi-god

    AustinIllini

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  16. Oletros macrumors 603

    Oletros

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    #17
    Excuse me?

    What has to do a divergent sum using an special notation (Ramanujan notation) with summing an integer to infinity?
     

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