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# The sum of all the positive integers = watch

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1. -1/12

Discuss.
2. meh?
3. no, you're wrong, it';s not negative!
4. (Original post by AntiMagicMan)
-1/12

Discuss.
The Sum of all +ve integers = +ve Infinity
5. . Try again. Do some research into the Riemann Zeta function and how s(-1) is evaluated.
6. s(-1) is outside the domain for which Euler's interpretation is valid. They've used "analytic continuation" to get -1/12 which doesn't really sound too hot...
7. Yep, thats right.

But in physical problems when the answer needs to take it into account this interpretation of the sum of all positive integers actually works and agrees with experimentation!
8. Seems pretty counter-intuitive that it's:
a) negative,
b) a fraction.

Doesn't the Reimann thing just deal with complex numbers anyways?
9. -1 is a complex number.
10. lol i think theres a thread for that http://www.uk-learning.net/t56272-2.html
11. Yes .
12. by the way, which physics problems need the sum of all positive numbers to equal -1/12?
13. Here's physicists for you
14. (Original post by beauford)
Here's physicists for you

?
15. Soz to resurrect a dead thread but which physics experiments need the sum to be -1/12 Magic?
Is it used in the Casmir effect?
Are there others?
16. (Original post by llduncanll)
Soz to resurrect a dead thread but which physics experiments need the sum to be -1/12 Magic?
Is it used in the Casmir effect?
Are there others?
Yes, Casimir effect needs it. Check out the Wikipedia for more (the paragraph called "Applications").
17. that the one where two plates of metal are attracted by quantum vacuum fluctuations? the weird just got weirder...
18. I don't see how the addition of an infinite number of +ve integers leads to a negative fraction when:

There are no -ve values in the addition
There are no fractional values in the addition

19. (Original post by mik1a)
that the one where two plates of metal are attracted by quantum vacuum fluctuations? the weird just got weirder...
Yup, that's the one. I must admit I dismiss quantum mechanics quite readily, because it's just too unreal for me.
20. (Original post by Invisible)
I don't see how the addition of an infinite number of +ve integers leads to a negative fraction when:

There are no -ve values in the addition
There are no fractional values in the addition

Yeh, common sense does seem to suggest it's wrong.

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