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Given a subset of the hyperbolic upper half plane, say an ideal triangle (so with vertices on the boundary), what is the cardinality of all points contained in the interior?

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    You might as well just ask: what is the cardinality of an open subset of $\mathbb{R}^2$? This is more general, and makes clear that there is not really any hyperbolic geometry in the question.2011-02-15

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