Infinite Venn diagram

\[\Large \bigcap_{n=1}^{m}A_{n} \neq \varnothing\]

If the above equation is true for all natural numbers \(m\), then must the following expression also be true? \[\Large \bigcap_{n=1}^{\infty}A_{n}\neq \varnothing\]

Details: \(A_1,A_2,A_3,\ldots \) are sets and \(\varnothing\) denotes the empty set.

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