We prove the geometric-progression case of the Erdős similarity conjecture. For every fixed $q\in(0,1)$ and every $\eta\in(0,1)$, we construct a compact set $E_{q,\eta}\subseteq[0,1]$ of measure greater than $1-\eta$ containing no nontrivial affine copy of $\{q^n:n\ge1\}$, for any translation and either sign of nonzero dilation. The set may depend on q; the result makes no simultaneous assertion for different ratios.

We construct a compact subset of the unit interval, of measure arbitrarily close to one, that contains no affine copy of the dyadic sequence $\{2^{-n}:n\ge1\}$. The conclusion holds for every translation and every nonzero real dilation, of either sign, proving the dyadic case of the Erdős similarity conjecture.