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The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a metric space. The dimension is drawn from the extended real numbers, <math>\overline{\mathbb{R}}</math>, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.

The Hausdorff dimension, more specifically, is a further dimensional number associated with a given set, where the distances between all members of that set are defined. Such a set is termed a metric space. The dimension is drawn from the extended real numbers, <math>\overline{\mathbb{R}}</math>, as opposed to the more intuitive notion of dimension, which is not associated to general metric spaces, and only takes values in the non-negative integers.

更具体地说，豪斯多夫维数是一个与给定集合相关联的更进一步的维数，其中定义了该集合所有成员之间的距离。这样的集合称为度量空间。维数是从扩展的实数，<math>\overline{\mathbb{R}}</math>，而不是更直观的维数概念，它不与一般的度量空间相关联，只接受非负整数的值。

更具体地说，豪斯多夫维数是一个与给定集合相关联的更进一步的维数，其中定义了该集合所有成员之间的距离。这样的集合称为度量空间。维数是从扩展的实数，<math>\overline{\mathbb{R}}</math>，而不是更直观的维数概念(它不与一般的度量空间相关联，只接受非负整数的值)。