given any reel number x there is an integer n such that n>x

Printable View

- Feb 16th 2009, 12:06 PMsah_mata proof at the beginning of analysis
given any reel number x there is an integer n such that n>x

- Feb 16th 2009, 12:16 PMJhevon
this is essentially asking for a proof of the

**Archimedean Property**: If $\displaystyle a>0$ and $\displaystyle b > 0$, then for some integer $\displaystyle n$, we have $\displaystyle na > b$.

i leave it to you to find the proof for this. chances are it is your text, if not (which would be strange) a quick web search should turn up results easily. it is a very famous property.

setting $\displaystyle a = 1$ and $\displaystyle b = x$ you have the claim you want to prove.

minor modifications are needed for the case $\displaystyle x \le 0$