I have the following exercise:
Prove that $A=\{(x,y)\in \mathbb{R}^{2} \mid x >0\}$ is a open set.
I try to solve that exercise with the help of definition, so :
To prove that $A$ is open, we show for every point $(x,y) \in A$ there exists an $r>0$ such that $D_{r}(x,y)\subset A$. Now I must know the definition for $D_{r}(x,y)$ and from the definition we find out that: $\displaystyle D_{r}(x,y)=\{(\alpha,\beta)\mid{(\alpha,\beta)-(x,y)
My question is: How do I prove that there is an $r>0$ such that $D_{r}(x,y) \subset A$ ?
Thanks :)