Sequence of Imaginary Reciprocals/Interior

From ProofWiki
Jump to navigation Jump to search

Theorem

Consider the subset $S$ of the complex plane defined as:

$S := \set {\dfrac i n : n \in \Z_{>0} }$

That is:

$S := \set {i, \dfrac i 2, \dfrac i 3, \dfrac i 4, \ldots}$

where $i$ is the imaginary unit.


No point of $S$ is an interior point.


Proof

From Sequence of Imaginary Reciprocals: Boundary Points, every $z \in S$ is a boundary point of $S$.

Thus no $z \in S$ is an interior point.

$\blacksquare$


Sources