(April 22, 2016 at 5:17 am)Alex K Wrote:(April 22, 2016 at 5:16 am)pocaracas Wrote: ooooOOO math geekiness!
The sum of all infinite positive natural numbers (1 + 2 + 3 + 4 + .... ) is a negative fractional number!! O.o
Silly String theorists are to blame. But this is only true if you mean by "1+2+3+4+5+6+" not ordinary naive summation but interpret it as a limiting case of representations of the Riemann zeta function. The ordinary series obtained by summing "1+2+3+..." is simply divergent.
Yes... the video does have a link to the Riemann Zeta function explanation...
But the one in there is still mind blowing...
However, the grain of salt starts with that first sum, 1-1+1-1+1-1.... = 1/2.... this is a limiting case, and not the ordinary series summation. The ordinary version would be just undefined.
