Astounding: 1+2+3+4+5+ = [not infinity]

  • #1
FlexGunship
Gold Member
369
8
[itex]
\displaystyle\sum_{n=1}^{\infty}{n} = {-}\dfrac{1}{12}
[/itex]


It seems that, regardless of intelligence, this proof (or sum, or proof of sum, or demonstration of sum) rattles some more than others. It is so astoundingly counter-intuitive that embracing it means really leaving your mathematical comfort zone.

Most objections to the resolution of this sum come from how uncomfortable people become when the sum of a series is not directly related to it's limit (or there is no limit, but there exists a sum).

I'll admit I'm not a PhD mathematician, so I'm not sufficiently skilled to dispute this on a mathematical level; however, I accept that algebraic operations can be performed on this infinite sum if for no other reason than that both the Casimir force (experimentally demonstrated) and string theory's critical dimension calculation (yet to be demonstrated) both require it.

This is the first time in my life that I've considered getting a tattoo. What a great reminder that reality is way more interesting than our intuition can handle. And FURTHER, that the only way for us to get our primate-brains to understand it is through rigorous application of science and math!

Here are the videos I had to watch before being even marginally convinced:

  1. Proof of Grandi's series
  2. Algebraic Demonstration
  3. Zeta-function Proof

https://www.youtube.com/watch?v=PCu_BNNI5x4
https://www.youtube.com/watch?v=w-I6XTVZXww
https://www.youtube.com/watch?v=E-d9mgo8FGk
 

Answers and Replies

  • #2
Office_Shredder
Staff Emeritus
Science Advisor
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