I have a cantor set F in (0,1) and its hausdorff dimension is dim_H (F)= \frac{1}{7} I have managed to show that dim_H (F \times [0,1])=\frac{8}{7}.

I am trying to determind dim_H (E) where E = ( F \times \Re) \bigcup (\Re\times F)

I have no clue how to do this or what E = ( F \times \Re) \bigcup (\Re \times F) actually means in terms of fractals.

Any help or explanations will be really appreciated.