The Sum of Two Cantor Sets

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The Cantor set is constructed iteratively. Starting with the closed unit interval , the open middle third is taken out, leaving the two closed intervals and . Then the middle thirds of those two intervals are taken out, leaving four intervals of length , and so on. The Cantor set is the limit (or intersection) of all such sets.

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Even though the Cantor set has measure zero and is nowhere dense, the set of sums where and are in is the whole interval , because the line always intersects the set .

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Contributed by: George Beck (March 2011)
Open content licensed under CC BY-NC-SA


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