Let $a \in \mathbb{R}$. I must prove:
$ \forall \epsilon \in \mathbb{R}^{>0}(0 \leq a<\epsilon) \to a =0$
Proof: If $a<\epsilon$ then $a< \epsilon +0$, by the property I have $a \leq 0$ and by hypothesis $a \geq 0$. Therefore $a=0$.
Is it correct?