TITLE: Hausdorff dimension of the p-adic integers
QUESTION [5 upvotes]: All Cantor sets are homeomorphic, but the Hausdorff dimension of a Cantor set depends on the particular metric being considered.  While there are some special situations where the Hausdorff dimension of a set can be computed easily, in general calculating Hausdorff dimension seems difficult.  I was wondering, however, if the Hausdorff dimension of the set of $p$-adic integers (which forms a Cantor set) is known for each $p$, and if so what a good reference for this would be.

REPLY [5 votes]: This question has been answered by Hagen von Eitzen in the comments:

The $p$-adic integers are the disjoint union of $p$ copies of itself scaled by a factor of norm $1/p$, hence the dimension should be $1$.