# Proof utilizing archemedian principle

• Feb 1st 2010, 05:24 PM
Pinkk
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. (Headbang)

EDIT: Bleh, nevermind. I figured it out.
• Feb 1st 2010, 05:52 PM
Drexel28
Quote:

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. (Headbang)

EDIT: Bleh, nevermind. I figured it out.

By the archimedean principle there exists an $n\in\mathbb{N}$ such that $\frac{1}{n}. Take $n'=\max\left\{a,n+1\right\}$.