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Thread: 1 + 2 + 3 + 4 + 5 + 6 + ... = -1/12

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    1 + 2 + 3 + 4 + 5 + 6 + ... = -1/12

    Posted this over at another forum. Thought you guys would appreciate it.

    Saw a video today which reminded me of this little gem:



    The issues that underlie the problems with this proof are complex, shall we say. I don't want to string you guys along, but since some of you are rather analytic, continuation of this sort of cryptic verbiage will likely be welcomed.

  2. #2
    Amen P-O's Avatar
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    My mind was boggled too when I first saw this. But replace S with "infinity" and now you see the problem.
    It's true that
    inf -inf = 4*inf= inf = 5 *inf +10*inf = 50*inf +4*inf.

    With this in mind, you can make S = any number that you want it to.
    Violence is never the right answer, unless used against heathens and monsters.

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    Quote Originally Posted by P-O View Post
    My mind was boggled too when I first saw this. But replace S with "infinity" and now you see the problem.
    It's true that
    inf -inf = 4*inf= inf = 5 *inf +10*inf = 50*inf +4*inf.

    With this in mind, you can make S = any number that you want it to.
    It isn't just S in that equation though, it's S and S2. You're presupposing that S is infinity, as well, which doesn't disprove anything; it's simply circular (or maybe not even that) reasoning. Not claiming the proof in the post above is valid, just that your reasoning for why it is invalid isn't appropriate.

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    Amen P-O's Avatar
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    When you use the algebra you use, you're presupposing that S is NOT infinite. That's the error.
    Violence is never the right answer, unless used against heathens and monsters.

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    Quote Originally Posted by P-O View Post
    When you use the algebra you use, you're presupposing that S is NOT infinite. That's the error.
    That simply isn't true. You. Are. Mistaken. Period. I mean no offense, but I'm holding fast here. Consider refreshing your memory on valid laws for infinite limits. There are clearly defined ways of dealing with infinity in algebra, and equalities still hold true under certain operations.

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    Amen P-O's Avatar
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    My first post shows why using the algebra you did, in the case of infinite quantities, is going to give meaningless results. If that's true, the validity of the proof rests on the fact that S is not infinite. Some moves are valid in the case of infinities, but the ones I highlighted aren't for reasons that I showed.

    Either the example I gave in the first post is wrong for some reason (please show me), or you have to show that S is not infinite before using that algebra.
    Violence is never the right answer, unless used against heathens and monsters.

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    It is equal to -1/12(R) not -1/12!

    https://en.wikipedia.org/wiki/Ramanu...vergent_series

    It is "not a sum in the traditional sense".

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    Quote Originally Posted by JohnClay View Post
    It is equal to -1/12(R) not -1/12!

    https://en.wikipedia.org/wiki/Ramanu...vergent_series

    It is "not a sum in the traditional sense".


    Technically the (R) there is simply used to denote the method of summation. That is, indeed, one way to find the sum of a divergent series. There are others, which I allude to in the OP.

  9. #9
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    Proof: S= 1/4

    S3 = S - 1
    S3 = 0+1+2+3+4...

    so,
    S = S-1

    Plugging in to your proof:

    S - S2 = 4S
    S-1-S2 = 4S
    1- 1/4 = 3S = 3/4
    S = 1/4
    Violence is never the right answer, unless used against heathens and monsters.

  10. #10
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    Quote Originally Posted by P-O View Post
    Proof: S= 1/4

    S3 = S - 1
    S3 = 0+1+2+3+4...

    so,
    S = S-1

    Plugging in to your proof:

    S - S2 = 4S
    S-1-S2 = 4S
    1- 1/4 = 3S = 3/4
    S = 1/4
    S - 1 <> 0 + 1 + 2 + 3 + 4 +...

    S - 1 = 2 + 3 + 4 + 5 + 6 + 7...

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