By definition, the characteristic of a field is the smallest number of times one must use the ring's multiplicative identity element (1) in a sum to get the additive identity element (0). Can we use the same rule for the set of natural numbers? If yes, I found a problem, that has something to do with the Riemann zeta function. If we calculate the sum for an infinity of identity elements, we obtain the sum of all natural numbers: 1+(1+1)+(1+1+1)+(1+1+1+1)+..., and, if we calculate this sum using the Riemann zeta function, we obtain . Do it 12 times and add one more multiplicative identity - what we obtain is exactly zero. Does this make sense? Or it is wrong right from the beginning?