# Math Help - Archimedean property

1. ## Archimedean property

Hello,

I'm preparing for a competitive exam which would include questions on the following topics.

i) Real number system as a complete ordered field
ii) Archimedean property

Can you please refer some website where I can get questions on these topics?

MAX

2. Originally Posted by MAX09
Hello,

I'm preparing for a competitive exam which would include questions on the following topics.

i) Real number system as a complete ordered field
ii) Archimedean property

Can you please refer some website where I can get questions on these topics?

MAX

What about books instead of sites? try Lang's "Algebra", or Dummit and Foote's "Abstract Algebra".

Tonio

3. Originally Posted by MAX09
Hello,

I'm preparing for a competitive exam which would include questions on the following topics.

i) Real number system as a complete ordered field
ii) Archimedean property

Can you please refer some website where I can get questions on these topics?

1) If $x\in\mathbb{R}$ and $x>0$, prove that there exists a unique $m\in\mathbb{N}$ such that $m-1\leq x< m$.
2) Prove that there exists a rational number between any two real numbers $x$ and $y$.