This is a homework question that I don't know where to start with it. Can somebody help me please? I am trying to work out the Hausdorff dimension of the set $\{0,1,\frac{1}{4},\frac{1}{9},...\}$.
I have worked this sort of thing out for a couple of fractal examples, but never for a set of numbers and I am pretty confused.
The Hausdorff dimension is defined in terms of covers. Try drawing out the points in this set - you'll notice that there's an accumulation point at $0$. If you place an interval of length $\delta$ just barely covering $0$, how many of the points in your set did you cover? How many intervals do you need to cover the remaining points? What does that tell you about the Hausdorff dimension, as you take $\delta$ to be arbitrarily small?