Archimedean Property

$\forall x,y\in R,x,y>0\Rightarrow \exists n\in N$ s.t $nx>y$ In other words, is a natural number $n$ when multiplied by $x$ is greater than $y$.

Other Thoughts

Given a large body of water, and you have a small cup of water. If you drop $n$ cups of water, you will eventually match that large body of water.

Reversed Archimedian Property

$\forall y\in R,y>0\Rightarrow \exists k\in N$ s.t $\frac{1}{k}\le y$

Proofs

• Archimedean Property Proof