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The Cantor set is closed, so its complement is open. So the complement can be written as a countable union of disjoint open intervals. Why can we not just enumerate all endpoints of the countably many intervals, and conclude the Cantor set is countable?

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    For an extremely convoluted madness on a similar topic, see my answer [here](http://math.stackexchange.com/questions/132022/formalizing-an-idea/132061#132061) and the comments that ensued.2012-10-10
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    @Asaf: **No-one** should be subjected to the reading of the comments on that answer.2012-10-10
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    @Arthur: I suggested to "Friedrich N." to read it when he's really bored. But I generally agree with your comment.2012-10-10
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    The set of endpoints of these countably many intervals is strictly contained in the Cantor set. The Cantor set is perfect and therefore uncountable.2012-10-10
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    @Arthur: Not even the Powers-That-Be at Hochschule Augsburg, where Prof. Dr. Wolfgang Mückenheim has been Professor since 1990 and for four years was Dean of the Faculty of General Sciences?2012-10-11
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    @Brian: If you think that would help I'd make an exception. But the good Herr Professor Doktor likely has them all enraptured by his "revolutionary" outsider status within the mathematics community. He doesn't exactly hide his "idio(t)syncratic" beliefs and I cannot imagine that the administration is ignorant of the fact that his take on mathematics stands in direct opposition to the overwhelming consensus of the vast majority within the community. (Either that or he will claim that someone is fraudulently using his name to discredit him.)2012-10-11
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    @Arthur: Sadly, I fear that you’re right.2012-10-11
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    The Cantor set is not only closed but also has empty interior. Maybe you had that in mind because this means that Cantor set equals it's own boundary and is thus equal to the boundary of the complement, a countable union of disjoint open intervals. The point is that the closure of this union is different from the union of the closures, and therefore the boundary of the complement, i.e. the Cantor set, contains many more points than the boundary points of those intervals.2012-10-11

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