The site's wording restricts $A$ to the positive integers; the problem the site and its sources mean concerns real sequences, and the two have opposite answers. What Erdős printed: both of Erdős's statements of the question, [Er61], item 31 of Part I, printed p. 238, and [Er64b], Part IV, item 4, printed p. 62, begin "Let $a_1<a_2<\ldots$ be an infinite sequence tending to infinity satisfying $a_{i+1}/a_i\to1$" and never make the $a_i$ integers, and the primary sources agree: LeVeque subdivides $(0,\infty)$ by real points $z_0<z_1<\cdots$ ([LV53], Section 1, p. 757), Davenport and Erdős take positive reals with $z_n\to\infty$ ([DaEr63], p. 3), Davenport and LeVeque take real $z_n\to\infty$ ([DaLe63], the Theorem, p. 315), and Schmidt a strictly increasing sequence of reals ([Sc69], p. 137). How the site's curator reads it: the label DISPROVED and the commentary, which credits Davenport and Erdős with the case $a_n\gg n^{1/2+\epsilon}$ and says that "the general conjecture is false, as shown by Schmidt [Sc69]", judge the real-sequence question, since Schmidt's counterexample has gaps tending to zero and says nothing about integer sequences, whose gaps are at least $1$, and since the sparse case would be redundant for integer sequences, all of which satisfy it; the problem's thread is empty, so the label and commentary are the whole of the ruling. Erdős's print and the curator's reading agree, and the integer restriction is the site's transcription alone. The answers differ. Under the site's wording, an infinite set of positive integers has at most $N$ members below $N$, so it meets the sparseness hypothesis of the Davenport--Erdős Theorem, at most $\ll N^{2-\delta}$ terms below $N$ for some fixed $\delta>0$, with $\delta=1$, and the deduction (9) that follows the Theorem ([DaEr63], p. 4) gives uniform distribution of $f(\alpha n)$ in $[0,1)$ for almost all $\alpha>0$: the site's wording is true for every such $A$, already for $A=\mathbb N$, where $f$ is the fractional part. Under the corrected Statement, Schmidt's Theorem 1 ([Sc69], p. 137) constructs a real sequence with $a_{i+1}/a_i\to1$ whose gaps tend to zero along which $f(\alpha n)$ is not uniformly distributed for almost every $\alpha>0$: the answer is no, and the standing judges this Statement. The change replaces "$\subseteq \mathbb{N}$ be infinite" by "$\subseteq \mathbb{R}$ be infinite, tending to infinity,"; "tending to infinity" is Erdős's own phrase, automatic for a set of integers but needed for reals, since the bounded sequence $a_i=2-1/i$ has $a_{i+1}/a_i\to1$ while $f(\alpha n)$ is undefined once $\alpha n\ge2$. Results about the site's wording, credited here: the sparse case of Davenport and Erdős (1963), which contains every set of integers by the one-line check above and is the partial claim on the corrected Statement on the Davenport--Erdős page; and the Lean theorem erdos_492 in Boris Alexeev's repository of Lean proofs, added on 2026-08-20 (file), written by the AI systems Codex and GPT-5.6 Sol, whose module docstring records that the counting hypothesis is automatic for integers; it proves the site's wording in full and a special case of the corrected Statement, so it is a claimed partial claim on Alexeev's page. That docstring is the earliest statement found here that the site's integer wording is true.