Largest and smallest D intersect E can be

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Homework Help Overview

The discussion revolves around the intersection of two sets, specifically D and E, within a defined interval around a point x0. Participants are exploring the largest and smallest possible values of the intersection D ∩ E.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the largest intersection being the interval [x0 - ε, x0 + ε] and question the smallest intersection, with some suggesting it could be the empty set. There is also a reflection on the underlying problem regarding accumulation points and limits.

Discussion Status

The discussion is active, with participants questioning their assumptions about the smallest intersection and clarifying the context of the problem. Some have indicated they have resolved parts of the problem, but there remains an exploration of the implications of their findings.

Contextual Notes

There is an indication that the problem involves conditions under which the interval may or may not be a subset of D, which affects the conclusions about the intersection.

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Homework Statement


Ok so I have D[tex]\cap[/tex][[tex]x_{0}-\epsilon,x_{0}+\epsilon[/tex]]=E[tex]\cap[/tex][[tex]x_{0}-\epsilon,x_{0}+\epsilon[/tex]].
I wnat to find the largest and smallest that D[tex]\cap[/tex]E can be.



Homework Equations





The Attempt at a Solution


For largest I got [tex][x_{0}-\epsilon,x_{0}+\epsilon][/tex]. I feel good about that, but I'm not so sure about smallest. I was thinking x0.
 
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Ok, I just realized the smallest = [tex]\oslash[/tex], right?
 
kathrynag said:
Ok, I just realized the smallest = [tex]\oslash[/tex], right?

Right, if [tex][x_0 - \epsilon, x_0 + \epsilon][/tex] is not a subset of D.
 
kathrynag said:
Ok, I just realized the smallest = [tex]\oslash[/tex], right?
Yes, which raises the question, "What was the problem, really?"
 
HallsofIvy said:
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.
 

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