The site's wording (accessed 2026-09-04; page last edited 2026-04-01) fails in two ways that the thread records. The site's revision of 2026-04-01 replaced $f(n)/F(n)\to0$ by $F(n)/f(n)\to0$ after thread comments of 2026-03-26 and 2026-03-27 showed that the earlier wording fails for every $f$: a fast-growing $F$, say $F(x)=x$, satisfies it and keeps the ratio bounded. The curator agreed on 2026-03-27 that [Er97] and [Er97e] carry the inverted ratio as a typo, while noting that [Er97] explicitly has the width of the interval tend to infinity faster than the normal order of $f$, so the correction there is more than a typo. A thread comment of 2026-07-24 shows that the current wording, read literally with $x$ a positive integer and $F$ real-valued, fails for every positive-integer-valued $f$: $F(x)=1/x$ has $F/f\to0$, and $(x,x+1/x)$ contains no integer, so the count is zero for every $x$; that is a thread comment, not a claim. The change adds $F(n)\to\infty$, the condition [Er97] carries as the curator describes it. The phrase "infinitely many $x$ such that the ratio tends to infinity" is read as a limit along a sequence of $x$: some short intervals receive many more values of $n+f(n)$ than their length. The site's commentary adds that [Er97] considers only $f$ growing more slowly than $(\log n)^{1-c}$ for some $c>0$.