# Why 1 is not a cluster point of $\frac1n$

I came across this definition of cluster point. Let $S \subset R$ be a set. A number $x \in \mathbb R$ is called a cluster point of $S$ if for every $\varepsilon > 0$, the set $(x−ε, x+ε)∩S \setminus \{x\}$ is not empty.

For the set $\{1/n:n∈\mathbb N\}$ why 1 is not a cluster point? I came across this proof while googling but still cant understand it

http://mathonline.wikidot.com/cluster-points