It is not well defined. Because an order of summation is not given you could just as easily sum pairs of (0,1), (-1,2), (-2,3), (-3,4)… (-x, x+1) and conclude you are constantly adding 1 to your total so it goes to infinity instead
Or do the reverse of (-1,0), (-2,1), … (-x-1, x) and get that the each pair adds -1 so the sum goes to negative Infinity
Order of the addition sometimes changes infinite sums. Infinitely large things are weird sometimes
0, because for every positive real number there’s a negative counterpart
It is not well defined. Because an order of summation is not given you could just as easily sum pairs of (0,1), (-1,2), (-2,3), (-3,4)… (-x, x+1) and conclude you are constantly adding 1 to your total so it goes to infinity instead
Or do the reverse of (-1,0), (-2,1), … (-x-1, x) and get that the each pair adds -1 so the sum goes to negative Infinity
Order of the addition sometimes changes infinite sums. Infinitely large things are weird sometimes