#### Proof on Cross Products of Two Fractals

By Shahin M Movafagh

**Theorem:**

Given A,B as two different Euclidean spaces and the
fractal dimension of A and B as dim(A) and dim(B) respectively; it will then
follow that the Cartesian product space dim(AxB) will be at least dim(A)+dim(B).

**Proof:**

**
**

Lets consider the specific example of A as the middle thirds Cantor set and
B as the middle second and four fifth Cantor set.

Given AxB={(x,y) in
:x
in A,y in B}, then AxB is the Cantor product or Cantor dust consisting of those
points in a plane with both coordinates in
: