# Math Help - Proof utilizing archemedian principle

1. ## Proof utilizing archemedian principle

Prove that if $a > 0$, then there exists $n \in \mathbb{N}$ such that $\frac{1}{n} < a < n$

I know the Archemedian Principle comes into play, but I'm just having a brain freeze on how to do this.

EDIT: Bleh, nevermind. I figured it out.

2. Originally Posted by Pinkk
Prove that if $a > 0$, then there exists $n \in \mathbb{N}$ such that $\frac{1}{n} < a < n$

I know the Archemedian Principle comes into play, but I'm just having a brain freeze on how to do this.

EDIT: Bleh, nevermind. I figured it out.
By the archimedean principle there exists an $n\in\mathbb{N}$ such that $\frac{1}{n}. Take $n'=\max\left\{a,n+1\right\}$.