Finding the Intersection of Infinite Sets: A Basic Set Theory Question

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SUMMARY

The discussion centers on finding the intersection of infinite sets defined by A(i) = [0, 1/i] as i approaches infinity. Participants confirm that the intersection of these sets results in the single point {0}. They clarify that if the sets were defined as A(i) = (0, 1/i), the intersection would be empty. The mathematical notation used is Intersect[A(i), {i,1,∞}] and \bigcap_{i=1}^{\infty} A(i).

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semidevil
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ok, find the intersection of i=1 to infinitie of A(i).

A(i) = [0, to 1/i].

I don't understand what it is asking. what do they mean to find the intersection of that?

and what if A(i) = [0, 1/n)
 
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To use mathematicasque notation, Intersect[A(i), {i,1,oo}] is the set of all points in each A(i). There's only one point in all A(i)'s: 0. Therefore the intersection is {0}. Same with the second one. But if they made it (0,1/i) then it would be empty.
 
Do you mean:

[tex]\bigcap_{i=1}^{\infty} A(i)[/tex]

where A(i) = [0, 1/i]? Wouldn't the answer be {0}?
 

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