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The following question came up in my 245A class today:
Is it possible to express a non-closed interval in the real line, such as [0,1), as a countable union of disjoint closed intervals?
I was not able to answer the question immediately, but by the end of the class some of the students had come up with an answer. It is actually a nice little test of one’s basic knowledge of real analysis, so I am posing it here as well for anyone else who is interested. Below the fold is the answer to the question (whited out; one has to highlight the text in order to read it).