It works more general for all the rationals.

Take it easy comrade, I'm aware

I think it is true that any subset of the rationals gives a box counting dimension \leq 1

It (subset of rationals) actually does.

The main point is that the Hausdorf dimension is zero. Because it is countable. Thefore, the Hausdorf dimension says it is not a fractal whereas the Boxcounting dimensions says it is a fractal.

I think I get where you are coming from.

It's nice learning from you anyways, thanks.