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\capE 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.