# closed ball

In the set of 3-adic numbers, the closed ball of radius 1/3 "centered" at 1 is the set $\{x | \exists n \in \mathbb{Z} . \, x = 3 n + 1 \}$. This closed ball partitions into exactly three smaller closed balls of radius 1/9, e.g., $\{x | \exists n \in \mathbb{Z} . \, x = 4 + 9 n \}$. Then each of those balls partitions into exactly 3 smaller closed balls of radius 1/27, and the sub-partitioning can be continued indefinitely, in a fractal manner.
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