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What is the Sum of the Natural Numbers? 1+2+3+4+... = ?

Opening Argument

What is the Sum of the Natural Numbers? 1+2+3+4+... = ?

1+2+3+4+5+...=?       

If you summed up all of the Natural Numbers, what would the answer be?  Would it equal Positive Infinity?  A positive Natural Number?  A positive Integer?  Could it equal a Negative Integer?

Also, do you think that a problem like this demonstrates that Mathematics is Bullsh't, maps onto Nature in interesting and counterintuitive ways, or other?  Could you imagine any applications to such a result?

Don't watch the videos until after you respond with your initial thoughts:  

B.  https://www.youtube.com/watch?v=0Oazb7IWzbA     (Side Note: I met the Mathematician in this video)

BryanMullinsTh1

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Arguments

  • 1+2+3+4+5=15.

    Enough said.
    I don't care how much more you add up, this will always add up to 15 until you add another number to it.
    DrCerealWilliamSchulz
  • 1+2+3+4+5=15.

    Enough said.
    I don't care how much more you add up, this will always add up to 15 until you add another number to it.

    The (...) indicates a continuation of the series through positive infinity
    WilliamSchulz
  • someone234someone234 153 Pts
    edited December 2017
    I do indeed think that problems like 0.9recurring being equal to 1, that 0 is not really even but also not odd and many other issues like square-rooting infinity (or even worse negative infinity) highlight precisely as you said: sometimes unapplied mathematics is not worth wracking your brain over.
    DrCereal
    I come to debate, I stay to troll,
    I leave to think, I return to brawl.
  • xMathFanxxMathFanx 83 Pts
    edited December 2017
    ------------------------Delete-----------------------------------
    BryanMullinsTh1
  • xMathFanxxMathFanx 83 Pts
    edited December 2017
    -----------------------------Delete-------------------------------------------
  • DrCerealDrCereal 99 Pts
    edited December 2017
    I've already seen this many times on the internet, and the intuitive answer is "infinity" though this is not considered an answer at all.
    The true answer is it's divergent (i.e., it has no bound), but you can do some mathematical trickery to make it equal -1/12.
    WilliamSchulz
    Bis das, si cito das.
  • I do indeed think that problems like 0.9recurring being equal to 1, that 0 is not really even but also not odd and many other issues like square-rooting infinity (or even worse negative infinity) highlight precisely as you said: sometimes unapplied mathematics is not worth wracking your brain over.
    Pure mathematics is beauty.
    Bis das, si cito das.
  • @DrCereal If ending up in a mental institution because of how insane the problem has driven you is worth the beauty then by all means go for it.

    Just because something is beautiful doesn't make it have relevance.
    I come to debate, I stay to troll,
    I leave to think, I return to brawl.
  • @DrCereal If ending up in a mental institution because of how insane the problem has driven you is worth the beauty then by all means go for it.

    Just because something is beautiful doesn't make it have relevance.
    There are mathematicians who have embraced pure mathematics and weren't driven insane by it.
    I never said it was relevant.
    Bis das, si cito das.
  • I don't care if you guys think it is infinite, I've only seen 1+2+3+4+5 which equals 15.

    Nothing much!
  • Depends on how many natural numbers you add. Adding all of them surely makes positive infinity, but Bryan does have a point that you haven't specified how many numbers are added on. It could be 15, it could be 1/100000000. Who knows?
  • Infinite series are always a mind tease. One of my favorites is the infinite sided polygon commonly known as a circle. That is, a square is a four sided polygon where the angle of two adjacent sides is 90 degrees. A polygon known as an octagon (8 sides, angle 135 degrees) the number of sides increases where the angle between two adjacent sides is greater than 90 degrees and less than 180 degrees.

    When the number of sides goes to infinity the angle between two adjacent sides goes to 180 degrees. So the question becomes, is a circle part of a straight line, or a straight line part of a circle? Perhaps, fuel for the “flat Earth” argument.

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