
1 + 2 + 3 + 4 + 5 + ... = -1/12 - anigbrowl
https://www.youtube.com/watch?v=w-I6XTVZXww
======
ivan_ah
Oy mate! Don't you have a pint of cider to drink in a cozy pub somewhere
instead of producing videos of such bollocks?

The series $\sum_{n=1}^\infty n$ is divergent, so you can't say anything about
its sum. For more info on the 1 - 1 + 1 - 1 +1 ... see:
[http://en.wikipedia.org/wiki/History_of_Grandi's_series](http://en.wikipedia.org/wiki/History_of_Grandi's_series)
This quote from the page is telling:

    
    
       G. H. Hardy dismisses both of these as "little more than nonsense."

~~~
mathnoob
It is not totally nonsense but the use of the benign sign = associating the
analytic continuation of a series where it converges to a place where it does
not without huge warning is not very rigorous.

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abc_lisper
Properties of numbers change at infinity. It is not conceivable to me, we can
use normal arithmetic operations on quantities tending to infinity. For
example, consider this...

    
    
       9999999999........... infinity
      -9999999999........... infinity
       -------------------------
       00000000000............ infinity
       -------------------------
    

Now, subtracting infinite numbers from infinite numbers should give a infinite
result. All we have is infinite zeros here, which cannot be inifinity.

~~~
kazagistar
You cannot understand "infinite numbers" without understanding how equality is
defined (bijection).

~~~
abc_lisper
Ok.. My post was a bait :).. Please tell me more or can you suggest me some
books i can read?

