User blog comment:Ynought/A question/@comment-35470197-20190602215451/@comment-35470197-20190603144406

Then for example, for any integer N, you can define a sequence b(N)_n converging to N in the following way:
 * 1) If n = 0, then b(N)_n = 1.
 * 2) Suppose n > 0.
 * 3) If b(N)_{n-1} <= N, then b(N)_n = b(N)_{n-1} + 1/n
 * 4) If b(N)_{n-1} > N, then b(N)_n = b(N)_{n-1} - 1/n.