Chapter 11.3, Problem 5E

Interpretation Introduction

Interpretation:

To find the similarity in the dimension of the subset of $\left[\text{0,1}\right]$ consisting of real numbers that can be written without the digit $\text{8}$ appearing anywhere in their decimal expansion.

Concept Introduction:

• If a self-similar set is composed of $\text{m}$ copies of itself scaled down by a factor $\text{r}$, then the similarity dimension $\text{d}$ is defined by:

  ${\text{m = r}}^{\text{d}}$, or $\text{d = }\frac{\text{ln m}}{\text{ln r}}$