Actually it's a fair nitpick because logarithmic density 0 does not imply natural density 0 - so the claim in the article is misleading in more than one way.
For example, the set of numbers with a perfect square number of digits has log density 0 but natural density non-existent (inf 0 and sup 0.9). I believe it holds in the other direction though - natural density 0 implies log density 0.
For example, the set of numbers with a perfect square number of digits has log density 0 but natural density non-existent (inf 0 and sup 0.9). I believe it holds in the other direction though - natural density 0 implies log density 0.