I have been reviewing my set theory and topology and recently came across an assertion I was not familiar with, and frankly have trouble grasping. In words,(adsbygoogle = window.adsbygoogle || []).push({});

let I be a set (which is to serve as the set of indices), then for each [itex]\alpha \in I[/itex] let [itex]A_\alpha[/itex] be a subset of some set S. Now, assuming I to be the null set:

[tex]\cup_{\alpha \in \emptyset} A_\alpha = \emptyset[/tex]

[tex]\cap_{\alpha \in \emptyset} A_\alpha =[/tex] S.

If someone could explain this to me, I would be grateful (only moderately grateful, mind you, so don't get any ideas). Or perhaps, point out the flaw in my reasoning, which follows. It seems to me that the union of, perhaps non-existent, subsets indexed by the empty set would be the empty set. However, assuming I followed that correctly, it seems to me that the intersection of these subsets would also be empty, yet apparently this is not the case, as the above asserts it is in fact S. Maybe I'm just horribly lost.

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# Problem with null indexed family of subsets.

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