Let $A\subseteq \mathbb{R}$ be an infinite set. Must there be a set $E\subset \mathbb{R}$ of positive measure which does not contain any set of the shape $aA+b$ for some $a,b\in \mathbb{R}$ and $a\ne 0$?

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Your question is exactly the **Erdős similarity problem / Erdős similarity conjecture**: an infinite set (A\subset\mathbb R) is called *universal (in measure)* if **every** measurable set (E\subset\mathbb R) with positive Lebesgue measure contains some nontrivial affine copy $aA+b$ [[nomath]](with $a\neq 0$)[[/nomath]]…

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.