# Largest and smallest D intersect E can be

1. Nov 15, 2008

### kathrynag

1. The problem statement, all variables and given/known data
Ok so I have D$$\cap$$[$$x_{0}-\epsilon,x_{0}+\epsilon$$]=E$$\cap$$[$$x_{0}-\epsilon,x_{0}+\epsilon$$].
I wnat to find the largest and smallest that D$$\cap$$E can be.

2. Relevant equations

3. The attempt at a solution
For largest I got $$[x_{0}-\epsilon,x_{0}+\epsilon]$$. I feel good about that, but I'm not so sure about smallest. I was thinking x0.

2. Nov 15, 2008

### kathrynag

Ok, I just realized the smallest = $$\oslash$$, right?

3. Nov 15, 2008

### Staff: Mentor

Right, if $$[x_0 - \epsilon, x_0 + \epsilon]$$ is not a subset of D.

4. Nov 16, 2008

### HallsofIvy

Staff Emeritus
Yes, which raises the question, "What was the problem, really?"

5. Nov 16, 2008

### kathrynag

It was a problem about accumulation points and proving there was a limit. I figured out the rest of the problem already. It was just that part.