This sequence is notable for including every integer exactly once—even 0 if one counts the empty partial sum—and thereby establishing the countability of the set Z {\displaystyle \mathbb {Z} } of integers.[2] The sequence of partial sums clearly shows that the series does not converge to a particular number (for any proposed limit x, we can find a point beyond which the subsequent partial sums are all outside the interval [x−1, x+1]), so 1 − 2 + 3 − 4 + ... diverges.