*T = 1+1+1+1+ ... = 1+(1+1+1+1+ ...) = 1+T Subtracting T from both sides, we have 0=1. QED.*
Now this is a neat mathematical demonstration for a postmodern approach to mathematics, physics and reality. How dare one say that 1+1=2? They are intolerant! I choose to believe that 1+1=1 And who are you to impose your belief system on me? :-) Nick On Tue, Jan 21, 2014 at 7:52 AM, Roger Hui <[email protected]>wrote: > I assume you are serious and not jerking people's chains. The sum that > these people are talking about does not use the classical definition of > infinite sums, which uses the concept of limits (for all epsilon>0, there > exists delta etc.). J does not subscribe to the alternative definitions. > > I have seen a YouTube video (search for "1+2+3+4") where two people > "proved" that +/1 2 3 4 5 ... equals %_12 and mentioned that the fact is > used in string theory. Whatever the methods that are used in string theory > to justify that that sum equals _12, their "proof" is, ahem, flawed. Using > the same logic, I can prove that 0=1: > > T = 1+1+1+1+ ... > = 1+(1+1+1+1+ ...) > = 1+T > > Subtracting T from both sides, we have 0=1. QED. > > Corollary: m=n for all positive integers m and n. > > > > > > > On Mon, Jan 20, 2014 at 9:23 PM, Richard Hill <[email protected]> > wrote: > > > The following statement is copied from Lubos Motl's physics blog... > > > > the sum of positive integers should be assigned the value \(-1/12\). > > However, this profound truth reigns not only in string theory but in any > > theory where some free fields periodically depend on two dimensions. > That's > > why one may verify that the sum equals \(-1/12\) even in QED, by > measuring > > the Casimir force between two plates. It's really an important insight in > > all of physics and all approaches to mathematics of functions that wants > to > > respect the same kind of "deep mathematical wisdom and elegance" that is > > exhibited by Nature through quantum field theory and string theory. > > > > He says this was known to Euler > > > > When I try it in J 604 > > > > I get > > +/i.@ _: > > ┌─────┬──┬──┐ > > │┌─┬─┐│i.│_:│ > > ││+│/││ │ │ > > │└─┴─┘│ │ │ > > └─────┴──┴──┘ > > but > > +/ i. 10E7 > > 5e15 > > And > > +/ i. 10E8 > > |limit error > > | +/ i.1000000000 > > Which is what I expected > > Is there any way the "profound truth" can be expressed in J? > > > > ---------------------------------------------------------------------- > > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
