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 > 1/2 > > 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! > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
