I have a bone to pick with the standard proof of the closed interval in R being compact with respect to the usual topology.(adsbygoogle = window.adsbygoogle || []).push({});

The proof starts out claiming that we can divide the interval in two and it is one of these two halves that is not coverable a finite subcollection of any open cover. Then we proceed to cut that interval in half and make the same claim and so on and so on.

The bone that I pick is what if both halves of the initial interval are uncoverable or both quarters of the initial half and so on.

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# [a,b] in R is compact

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