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Examples* The Euclidean space Rn has Hausdorff dimension n. * Countable sets have Hausdorff dimension 0. * Fractals typically have fractional Hausdorff dimension, whence the name. For example, the Cantor set is a union of two copies of itself, each copy shrunk by a factor 1/3; this fact can be used to prove that its Hausdorff dimension is ln(2)/ln(3) (see natural logarithm). |
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