This is a statement my professor made in class some time ago (as a means to show that C contains a Hamel basis) that seemed fairly innocent, but it's bothered me for awhile. I did some searching online, and it seems that C+C=[0,2]. There it was again stated that this is fairly easy to show, but they neglected to give any insight as to how one might show it. Is there something simple I'm missing?(adsbygoogle = window.adsbygoogle || []).push({});

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# If C is the Cantor set, C+C contains an open set.

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