Say there's a family of set M with infinitely many elements with the property that whenever X and Y belong to M, so does their intersection. How to justify that the intersection of all elements in in M, N, (interpreted here as the largest subset common to every element in M) is also in M? Since N can't be constructed in finite number of steps, I'm having trouble seeing what justifies the conclusion. Maybe there's a way to establish the existence of two elements in M whose intersection is exactly N?(adsbygoogle = window.adsbygoogle || []).push({});

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# Intersection of all sets in a family of sets

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