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

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The discussion centers on finding the intersection of the sets A(i) defined as [0, 1/i] for i from 1 to infinity. Participants clarify that the intersection consists of all points common to each A(i), which ultimately leads to the conclusion that the only point in all sets is 0. Therefore, the intersection is {0}. If the sets were defined as (0, 1/i), the intersection would be empty. The mathematical notation for this intersection is correctly represented as ∩_{i=1}^{∞} A(i).
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:

\bigcap_{i=1}^{\infty} A(i)

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