Infinite Intersection!

Algebra Level 3

\[\large(-1,1) \cap (-\frac{1}{2}, \frac{1}{2}) \cap (-\frac{1}{3}, \frac{1}{3})\cap\cdots = \{a\}\]

Where \((m, n) = \{ x \in \mathbb R | m<x<n \}\)

For example: \((-1, 1) = \{ x \in \mathbb R | -1<x<1\}\)

where \(\mathbb R\) is set of real numbers.

"Enter your answer as the value of \(a\).

The above gives a classic example of "arbitrary i.e. infinite" intersection of open sets 'need not' be open in \(\mathbb R\).


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