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There is a standard definition of what '=' means and your equation does not satisfy it. https://www.youtube.com/watch?v=YuIIjLr6vUA https://www.youtube.com/wat

There is a standard definition of what '=' means and your equation does not satisfy it. https://www.youtube.com/watch?v=YuIIjLr6vUA https://www.youtube.com/watch?v=YuIIjLr6vUA

carterehsmith 9y ago
You say "your" and yet, this has nothing to do with me. I pointed to the wikipedia article. BTW this result is not exactly new, and it has specific confirmation in physics. You cannot argue that with high-school math. There is more to it.
- twiceaday 9y ago
  The bit on Wikipedia that follows the equation is part of the equation. It is the context that explains how to compute it. You need that bit because the equation uses extremely common syntax as short-hand for an operation that is different from the common one. If you write it in a way that doesn't rely on redefining common syntax like so "ζ(-1) = -1/12" it seems a lot less interesting doesn't it? Perhaps syntax confusion is the only interesting thing to it.
  - carterehsmith 9y ago
    There is more to it - the number -1/12 actually pops up in physics when doing something awfully similar to 1+2+3... This may be useful: https://motls.blogspot.ca/2014/01/sum-of-integers-and-oversold-common.html https://motls.blogspot.ca/2014/01/sum-of-integers-and-overso... " The real problem is that the definition of the sum involving the limit of partial sums – limits that way too often "diverge" or "refuse to exist" – isn't the only definition or the best definition or the most natural definition that may be connected to the sum. There exist better definitions of the infinite sum – numerous definitions that turn out to be more natural in physics applications – and they generally produce the result −1/12−1/12. It is no trick or sleight-of-hand. The value −1/12−1/12 is really the right one and the rightness may be experimentally verified (using the Casimir effect). "
    - kazinator 9y ago
      The ordinary sum of any collection of positive integers is not a fraction, let alone a negative one. If we take the set { 1, 2, 3, ... 4 } the summation or partial summation of no subset of this set, finite or not, converges on any fraction or negative number. No matter what order we choose for traversing that set for generating a series, we never see anything resembling -1/12 as a partial sum or limit. The ordinary arithmetic sum of any collection of positive integers is an integer which is strictly greater than each the integers. The pages you're referencing are all crackpottery.
      - carterehsmith 9y ago
        >> The pages you're referencing are all crackpottery. So... I can trust Ramanujan and Abel, that published results on these things, and Terrence Tao that has a nice writeup, and a bunch of others, or I can trust HN user "Kazinator", who... published some middle-school algebra "proof" on HN. Guess who is crackpot here. >> https://en.wikipedia.org/wiki/Ramanujan_summation https://en.wikipedia.org/wiki/Ramanujan_summation
        kazinator 9y ago
        I would say, it is he who cannot separate "summation" from "Ramanjuan summation" due to the overlapping notation.
        carterehsmith 9y ago
        There are different definitions of "summation". Also different definitions of "integration". I can see how overlapping notation can be confusing for laymen (me included). But that does not mean that people that came up with those are crackpots, just because they reused the "=" symbol.
        deleted 9y ago
        [deleted]
        9y ago

There is a standard definition of what '=' means and your equation does not satisfy it. https://www.youtube.com/watch?v=YuIIjLr6vUA https://www.youtube.com/watch?v=YuIIjLr6vUA

carterehsmith 9y ago

You say "your" and yet, this has nothing to do with me. I pointed to the wikipedia article. BTW this result is not exactly new, and it has specific confirmation in physics. You cannot argue that with high-school math. There is more to it.

twiceaday 9y ago
The bit on Wikipedia that follows the equation is part of the equation. It is the context that explains how to compute it. You need that bit because the equation uses extremely common syntax as short-hand for an operation that is different from the common one. If you write it in a way that doesn't rely on redefining common syntax like so "ζ(-1) = -1/12" it seems a lot less interesting doesn't it? Perhaps syntax confusion is the only interesting thing to it.
- carterehsmith 9y ago
  There is more to it - the number -1/12 actually pops up in physics when doing something awfully similar to 1+2+3... This may be useful: https://motls.blogspot.ca/2014/01/sum-of-integers-and-oversold-common.html https://motls.blogspot.ca/2014/01/sum-of-integers-and-overso... " The real problem is that the definition of the sum involving the limit of partial sums – limits that way too often "diverge" or "refuse to exist" – isn't the only definition or the best definition or the most natural definition that may be connected to the sum. There exist better definitions of the infinite sum – numerous definitions that turn out to be more natural in physics applications – and they generally produce the result −1/12−1/12. It is no trick or sleight-of-hand. The value −1/12−1/12 is really the right one and the rightness may be experimentally verified (using the Casimir effect). "
  - kazinator 9y ago
    The ordinary sum of any collection of positive integers is not a fraction, let alone a negative one. If we take the set { 1, 2, 3, ... 4 } the summation or partial summation of no subset of this set, finite or not, converges on any fraction or negative number. No matter what order we choose for traversing that set for generating a series, we never see anything resembling -1/12 as a partial sum or limit. The ordinary arithmetic sum of any collection of positive integers is an integer which is strictly greater than each the integers. The pages you're referencing are all crackpottery.
    - carterehsmith 9y ago
      >> The pages you're referencing are all crackpottery. So... I can trust Ramanujan and Abel, that published results on these things, and Terrence Tao that has a nice writeup, and a bunch of others, or I can trust HN user "Kazinator", who... published some middle-school algebra "proof" on HN. Guess who is crackpot here. >> https://en.wikipedia.org/wiki/Ramanujan_summation https://en.wikipedia.org/wiki/Ramanujan_summation
      - kazinator 9y ago
        I would say, it is he who cannot separate "summation" from "Ramanjuan summation" due to the overlapping notation.
        carterehsmith 9y ago
        There are different definitions of "summation". Also different definitions of "integration". I can see how overlapping notation can be confusing for laymen (me included). But that does not mean that people that came up with those are crackpots, just because they reused the "=" symbol.
        deleted 9y ago
        [deleted]
        9y ago