Archimedean Property

Definition

$\forall ϵ>0,\exists n\in \mathbb{N},\frac{1}{n}<ϵ$

For any positive real number $ϵ$, there exists a positive integer $n$ such that $\frac{1}{n}$ is less than or equal to $ϵ$

Proof

Let $\forall n\in \mathbb{N},\frac{1}{n}\ge ϵ$, then $\frac{1}{ϵ}\ge n$ Since $\mathbb{N}$ is not bounded above, It is a contradiction