Largest and smallest D intersect E can be

  • Thread starter kathrynag
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In summary, The conversation is about finding the largest and smallest possible values for the intersection of sets D and E within a given range. The largest value is determined to be [x_{0}-\epsilon,x_{0}+\epsilon], while the smallest value is determined to be \oslash if the given range is not a subset of D. The conversation also touches on the nature of the problem being discussed, which involves accumulation points and proving a limit.
  • #1
kathrynag
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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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  • #2
Ok, I just realized the smallest = [tex]\oslash[/tex], right?
 
  • #3
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.
 
  • #4
kathrynag said:
Ok, I just realized the smallest = [tex]\oslash[/tex], right?
Yes, which raises the question, "What was the problem, really?"
 
  • #5
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.
 

1. What is the largest possible intersection between two sets, D and E?

The largest possible intersection between two sets, D and E, is when the two sets are identical. In other words, when D and E have the exact same elements.

2. Is there a limit to how large the intersection between two sets can be?

Yes, there is a limit to how large the intersection between two sets can be. The limit is equal to the size of the smaller set between D and E.

3. Can the largest intersection between two sets be infinite?

No, the largest intersection between two sets cannot be infinite. This is because both sets have a finite number of elements, and the intersection can only include elements that are present in both sets.

4. What is the smallest possible intersection between two sets, D and E?

The smallest possible intersection between two sets, D and E, is when the two sets have no elements in common. In other words, when the intersection is an empty set.

5. Is it possible for the smallest intersection between two sets to have negative elements?

No, the smallest intersection between two sets cannot have negative elements. This is because the intersection only includes elements that are present in both sets, and negative elements are not present in either set.

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