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According to Eureka Seven, to end existence, all you have to do is make too many things think at once... thus reaching the limit of questions and causing the universe to overload. Dewey, the Big Bad almost succeeds, by waking up the dormant aliens that have covered the earth's crust.
Though this seems to happen only in the anime, where the thoughts have mass (the trapar is made of the dreams of the dormant Coralian crust). In the manga, the limit of questions is never mentioned. The motivations of the Coralians are very different, too.