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I just learned that the set [a,a) is not a proper subset of itself. So if In=[a,a), In+1 can't satisfy In+1 < In.
Now I have no idea what's going on. If no In can be empty, how can the intersection of all In be empty in any case! HELP
Hi. Thanks for the response. Based on your definition [a,a) is indeed empty. Although I'm not sure why you think the question requires the endpoints to be distinct.
If every set In+1 is a subset of In, then the only way the intersection of In for all n is empty is if one of those sets is...
question about the set [a,a)
If S=[a,a) Can such a set exist? It implies that a is in S and not in S, which doesn't make sense, but it seems a problem I'm trying to do requires it to be considered empty.
The question is:
Let In = [an,bn) where
In+1 < In for all natural numbers n. [<...
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