On Fri, Feb 28, 2014 at 7:03 PM, James Propp <jamespropp@gmail.com> wrote:
Dan, can you say more about why you object to using the equation 1+2+3+4+...=-1/12 in this way? Is this equation, for you, exactly as objectionable as (say) 1+2+4+8+...=-1, and for the exact same reason?
And is that reason the conviction that "1+2+3+4+..." must (in the absence of side explanations) connote the limit (in Cauchy's sense) of 1+2+...+n as n goes to infinity?
I would guess his objection has to do with abuse of notation, in that one is implicitly assuming a nontrivial summation method. Are there series whose sum gives different results if you use Abel, Borel, Cesaro, Euler, or Lambert summation? If not, then perhaps the objection is unfounded. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com