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I saw a post in Quora that stated the above. I'm wondering how come we get a negative I know that the sum is approaching infinity. Does that mean that infinity means approaching zero ? No right? Because infinity in my point of view, just means increasing without bounds. Anyways. am I correct? I always though of infinity more of a concept rather than a number. If anyone can explain why is this, I would really appreciate it.

Arnaldo
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Julio Rosario
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  • You're correct, it does increase without bounds. Can you post a link to the Quora post? – Franklin Pezzuti Dyer May 08 '17 at 19:50
  • This is related to the Riemann Zeta function, and how it can be used to evaluate some divergent series. – mathfan27543 May 08 '17 at 19:52
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    do you know the mysterious "google"? https://www.google.de/search?q=1%2B2%2B3%2B4&ie=utf-8&oe=utf-8&client=firefox-b&gfe_rd=cr&ei=TMwQWYy5EqHi8Af34o2wBQ – tired May 08 '17 at 19:52
  • In a word: No, this identity is false. However there are some facts about the Riemann zeta function that some choose to interpret as this identity. – Jair Taylor May 08 '17 at 20:31
  • As a series $\sum_{n\ge 1} n = \infty$ but $\displaystyle\overset{\mathcal{Z}}{\sum_{n\ge 1}} n = -1/12$ where $\displaystyle\overset{\mathcal{Z}}{\sum}$ means the zeta-regularized summation, completely changing the meaning of the symbol $\sum$. See https://en.wikipedia.org/wiki/Divergent_series#Zeta_function_regularization – reuns May 08 '17 at 22:12
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    A general comment: life is short ! Dont spend time on such mathematical hoaxes. There are so many beautiful "true" mathematics :) – Jean Marie May 09 '17 at 00:31
  • Short, wonderful coverage of this topic by 3Blue1Brown (also tons of other cool math things on his channel): https://www.youtube.com/watch?v=sD0NjbwqlYw – JoseOrtiz3 Feb 16 '18 at 21:56

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