Originally Posted by

**rebghb** Hello everyone!

I'm new to the amazing world of analysis. I've got a question related to boundedness.

A set $\displaystyle A$ is bounded in $\displaystyle R$ if there exists two real numbers $\displaystyle a$ and $\displaystyle b$ such that $\displaystyle A\subset [a,b][$.

Well since we're talking about $\displaystyle R^1$, we can't differentiate between and open ball and a 1-cell, but when we're talking about boundedness in the complex plane $\displaystyle R^2$ for instance, must the set $\displaystyle A$ of points $\displaystyle P(x,y)$ be $\displaystyle a_1 < x < a_2$ and $\displaystyle b_1 < y < b_2$ or is it that $\displaystyle d(p,q) = |p-q| < r$ for some $\displaystyle q$??

Thanks!!