The full question reads: Suppose that $a$ is a number that has the property that for every $n \in \mathbb{N}$, $a \leq 1/n$. Prove $a \leq 0$.
Is there anyway to show this using Archimedean Property, or is it something related to the Completeness Axiom? The problem using the Archimedean Property is that I get up to $a< \epsilon$ but from there I am not able to conclude anything about whether $a \leq 0$ because $\epsilon > 0$.