Hausdorff dimension of the Cantor Set

[alpar_r]

Hi everyone!

I am thinking about, how can calculate the Hausdorff dimension of the Cantor set? I know, that this dimension is $$\frac{\log 2}{\log 3}$$ but I cannot prove it.

Any ideas?

 

[g_edgar]

Of course you will need to use the definition of Hausdorff dimension. In one popular proof, you do it in two parts: One shows the dimension is <= log 2/log 3 and the other shows the dimension is >= log 2/log 3 . But of course both of them need the definition!