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  1. #21
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    Quote Originally Posted by Anarch Son of Gods View Post
    The thing is that there is a lot of questionable methods he uses to explain this mathematically (but there is also a link in the video to more conventional methods to come to the same conclusion).
    Pretty much this. I might even give an elementary proof here, if someone wants to see it.

  2. #22
    Quote Originally Posted by Trigg View Post
    what's really niggling me is, why does he push the 2nd part of 2S+2S along? I can't see an explanation of why he does that but doesn't for S-2S. I assume there's a rule in maths for doing this?
    Simply put 1+1+1 = 3 , 2 + 4 + 6 = 12

    1 + 1 + 1
    0 + 2 + 4 + 6
    -----------------
    1 + 3 + 5 + 6 = 15

    You can add any terms to any terms in a sum and get the same answer (added the 0 + to preserve indentation).

    - - - Updated - - -

    Quote Originally Posted by Reliefpfeiler View Post
    Pretty much this. I might even give an elementary proof here, if someone wants to see it.
    Go for it... I'd welcome it. Just keep it simple

    - - - Updated - - -

    Quote Originally Posted by Templar 331 View Post
    Which is where I got the quotes from that refute the claim that infinity = -1/12.
    Never said infinity = -1/12 ...

  3. #23
    Elemental Lord Templar 331's Avatar
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    Quote Originally Posted by schwarzkopf View Post
    Simply put 1+1+1 = 3 , 2 + 4 + 6 = 12

    1 + 1 + 1
    0 + 2 + 4 + 6
    -----------------
    1 + 3 + 5 + 6 = 15

    You can add any terms to any terms in a sum and get the same answer (added the 0 + to preserve indentation).
    The difference here is those equations have a definite answer. Infinity doesn't.

    - - - Updated - - -

    Never said infinity = -1/12 ...
    It's in the title of the thread.

  4. #24
    Quote Originally Posted by Templar 331 View Post
    It's in the title of the thread.
    Oh really... I don't see it at all. Matter of fact, neither the word nor any hint of the word 'infinity' is used in the title.

  5. #25
    This thread is literally 2004 /b/-tier trolling - and MMO-C is going to carry it to page 100.

  6. #26
    Herald of the Titans
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    Maybe we can get another 50+ page thread (that's the last time I looked at it) about something that has no relevance to 99.999% (or is that 100%?) of people.

  7. #27
    Quote Originally Posted by g01851 View Post
    Maybe we can get another 50+ page thread (that's the last time I looked at it) about something that has no relevance to 99.999% (or is that 100%?) of people.
    This one is entertaining, recreational maths at its best in my opinion. Sure it has advanced uses - but if you look at the numberphile.com videos, they are all entertaining.

  8. #28
    No. This is an abuse of notation.

    For certain values, the Riemann Zeta function is equivalent to the geometric series. But when you analytically extend it, you're appending extra values to the Riemann Zeta. It is not the geometric series for these new values.

    It's bad notation designed to confuse, used by lazy mathematicians and physicists who don't give a fuck. It pretty clearly flies in the face of the fact that the series diverges. But how can the series diverge and equal -1/12 at the same time? Because you aren't summing the series when you reach the -1/12 conclusion. It's just bullshit notation through and through.

    The .999.... = 1 thing? Nobody disputes that. This shit? I took this to math professors at my institution (one of the strongest math programs), and they essentially all waved it off as crappy, nonsense notation.
    Quote Originally Posted by Zantos View Post
    There are no 2 species that are 100% identical.
    Quote Originally Posted by Redditor
    can you leftist twits just fucking admit that quantum mechanics has fuck all to do with thermodynamics, that shit is just a pose?

  9. #29
    Deleted
    Quote Originally Posted by schwarzkopf View Post
    Go for it... I'd welcome it. Just keep it simple
    OK, I'll try. It's not complete atm, but whatever.
    So for Re(s)>1, the series Sum[n in N](1/n^s) converges. We want to analytically extend it to s=-1. To achieve this, we manipulate it: For Re(s)>1,
    lim[N -> infinity] (Sum [n= 1, ..., N] (1/n^s) - 1 / ((s-1) N^(s-1)) - 1 / (2N^s) - s / (12 N^(s+1))) is the same (the latter terms converge to zero). We can extend this definition easily, for s=-1, we get: lim[N -> infinity] (Sum [n= 1, ..., N] (n) + N^2 / 2 - N/2 - 1/12) = -1/12.

    Why these "arbitrary" terms? Because the whole thing can be extended easily (as a converging limit) to Re(s)>-2. For an account of the asymptotic behaviour of Sum [n= 1, ..., N] 1/n^s, as n -> infinity, you'd have to read through this for now (which is also why the terms have to be that way). I'll see if I can provide an easily digested "proof" of it.

    @ Garnier: Yeah, it's really bad notation, but we know how it should be written down.

  10. #30
    Also, I'm watching the video again and /sighhhhhhhh

    "The sum is 1/2." No. No. The Cesaro sum is 1/2. By not explicitly mentioning that they're using a different summation method, they're essentially tricking people into believing that if you add 1's and -1's in the conventional way, you'll arrive at 1/2. Which is obviously false. Never mind that the essentially handwaved it after giving an intuitive argument.

    And second, the addition of infinite series is which don't converge is itself ill defined in the sense that they're using it. For instance, if you go back to the 1 - 1 + 1 -1 ...... and you stick zeros in between every two numbers, you get a Cesaro sum of 2/3. So why don't Numberphile call the sum 2/3? I mean, it's the same thing in the simple way they're presenting it. Did I just prove that 1/2 = 2/3?
    Quote Originally Posted by Zantos View Post
    There are no 2 species that are 100% identical.
    Quote Originally Posted by Redditor
    can you leftist twits just fucking admit that quantum mechanics has fuck all to do with thermodynamics, that shit is just a pose?

  11. #31
    Quote Originally Posted by schwarzkopf View Post
    Nope ... because an expert can explain something better than a wall of text.

    You go to the wall of text to get the details, you go to an expert to get an explanation.

    I provided the explanation, you provided the details - between the two of us, I think we have all bases covered.
    Numberphile isn't an expert on mathematics. He's a guy on youtube.

    Somebody can make probably about a hundred grand a year with catchy viral videos. Whereas the sky is the limit if somebody is an actual expert at something.

    So if he was an expert he wouldn't be on fucking youtube.

  12. #32
    Immortal Zelk's Avatar
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    The guy needs to learn to brush his teeth before he does anymore of these videos.

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