Largest and smallest D intersect E can be

[kathrynag]

Homework Statement

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.

Homework Equations

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.

 

[kathrynag]

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

 

[Mark44]

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

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

 

[HallsofIvy]

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

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

 

[kathrynag]

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

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.