Abstract
Erdős posed the following problem. "Let $E$ be an infinite set of real numbers. Prove that there is a set of real numbers $S$ of positive measure which does not contain a set $E^\prime$ similar (in the sense of elementary geometry) to $E$.'' The proof is known for only a few special cases; and not included among these is the geometric sequence $\{2^{-n}\}_{n=1}^\infty$. In this paper we examine the known literature, present some new results, and ask a few related questions.
Citation
R. E. Svetic. "The Erdős Similarity Problem." Real Anal. Exchange 26 (2) 525 - 540, 2000/2001.
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