Analysis · Oct 6, 2026

The geometric case of the Erdős similarity conjecture

For every fixed q∈(0,1)q\in(0,1), constructs compact subsets of [0,1][0,1] with measure arbitrarily close to one containing no translated and nontrivially dilated copy of {qn:n≥1}\{q^n:n\ge1\}, with dilations of either sign. This resolves the geometric-progression case of the Erdős similarity conjecture for every ratio.

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