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RE: The paradoxical cake of Cantor
altough the Cantor cake is constructed by removing cake-intervals it is not equal to a collection of intervals. Thus, it transcends the natural intuition that we have for intervals.
I find this in particular really interesting. I had never thought about it like that! I'll try to dig a little into Cantor's work for better understanding since right now this is a little above me.
Great post!
Thanks as always for your support.
So it even gets crazier because in a sense there are the same amount of distinct points in a Cantor set as there are on the real line. (Or more formally, the cardinality of the Cantor set and the real line is the same)