That's pretty much what I thought. The idea that the sum of such a series
*equals* 1/2 I think is only one way to make sense of it. Who says that a
rational number is even an option? What if +1 and -1 are absolute, like
'moving' and 'static'. There is no 1/2 moving. Still, it's interesting to
ponder the meaning of -1/12.
On Friday, January 17, 2014 8:27:42 PM UTC-5, Liz R wrote:
> The demonstration that the sum of the positive integers is -1/12 relies on
> the assumption that the sum of
> 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 .... is
> However that is by no means certain. The sum could be undefined, in which
> case the proof simply fails. Or it could be one of the other values
> mentioned - if it's 0, we get the sum of the positive ints is either 0 or
> infinity (because S = 4S). If it's 1, we get the sum of the pos int = -1/6!
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