Originally Posted by

**Drexel28** That would certainly be "strange and creative"! That's exactly the kind of thing I wanted to see. But, I have a few problems:

A) I know so little about what you just said that I only *think* you are talking about fractals (I know who Benoit Mandelbrot is)

B) I think you're idea involves discussing a sequence of connected sets $\displaystyle \left\{F_n\right\}_{n\in\mathbb{N}}$ such that $\displaystyle F_n\to\mathbb{D}$. What does convergence mean for a sequence of sets? Secondly if I take a heuristic idea of what that would mean a reasonable counterexample to a sequence of connected sets converging to a connected sets would be $\displaystyle F_n=\left(-1,\tfrac{1}{n}\right)\cup\left(\tfrac{-1}{n},1\right)$ since each $\displaystyle F_n=(-1,1)$ is connected but $\displaystyle F_n\to (-1,0)\cup(0,1)$ which is not. Does that maybe capture an idea of converging of a sequence of sets?