Sequence of Imaginary Reciprocals/Closure

Theorem
The closure of $S$ is the set:
 * $\set {0, i, \dfrac i 2, \dfrac i 3, \dfrac i 3, \ldots}$

Proof
By definition, the closure of $S$ is the set $S$ along with all its limit points.

Sequence of Imaginary Reciprocals: Limit Points, $S$ has one limit point $z = 0$.

Hence the result.