Read as printed, the condition $\lvert B\rvert=g(n)$ asks for a subset of exactly $g(n)$ elements in every instance, and then no $g(n)$ exists once $n$ is large: for $A=\{2,\ldots,n+1\}$ and $I=\{1,\ldots,n+1\}$ the interval has only $n+1$ elements, which caps $g(n)$ at $n+1$, while the 1959 lower bound gives instances that need more than $(2-\varepsilon)n$ selected elements, so neither displayed bound holds as worded (Progress). The change replaces $\lvert B\rvert=g(n)$ by $\lvert B\rvert\le g(n)$; nothing else changes. The evidence is the convention the sources assume: Erdős and Surányi (1959), section 1, p.39, fixes the interval at the largest given integer and asks how many of its integers must be selected, and section 9, p.44, and the summaries, pp.47-48, bound that selected count from below by $(2-\varepsilon)n$; Erdős (1992), p.34, uses the same loose exact-number wording for the least number of integers one can find, and its equation (1) is the same lower bound on that count. Lech Mazur posted the exact-size failure in comment 6301, 6 May 2026, attributing the observation to GPT-5.5 Pro. The page's standing judges the corrected Statement.