> From: Chat [mailto:[email protected]] On Behalf Of Raul > Miller > Sent: dinsdag 12 april 2016 15:38 > > On Tue, Apr 12, 2016 at 6:38 AM, R.E. Boss <[email protected]> wrote: > > Sorry my answer took a while, but I attended a lecture on "Infinite > bookkeeping", from which I learned that > > 1-1+1-1+1-1+1-1+1-1+.....= 1r2 (the dots meaning 'ad infinitum') and > > 1-2+3-4+5-6+.... = _1r4 , > > unfortunately this cannot be experienced with J. > > Well... https://plus.maths.org/content/infinity-or-just-112 touches on > this subject.
The lecturer and (some of) his audience knew both the site and the youtube it mentions. So he pointed out what you are – mathematically – allowed to do with divergent sums. Let s= a1+a2+a3+....then allowed are 1) s=0+a1+a2+a3+.... 2) k*s= k*a1+ k*a2+ k*a3+.... 3) if t=b1+b2+b3+... then s+t=(a1+b1)+(a2+b2)+(a3+b3)+... (the last rule I don't remember right now) So you get s=1-1+1-1+1-1+1-1+1-1+..... s=0+1-1+1-1+1-1+1-1+1-1+..... 2s=1, so s=1r2. But watch out: what is 1-1+0+1-1+0+1-1+0+....? Well, same trick s=1-1+0+1-1+0+1-1+0+.... s=0+1-1+0+1-1+0+1-1+0+.... s=0+0+1-1+0+1-1+0+1-1+0+.... so we get 3s=1 and thus s=1r3 (!) I loved that. R.E. Boss ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
