I'm working with non decreasing functions $f:\mathbb{N}\rightarrow\mathbb{N}$ such that for any $g:\mathbb{N}\rightarrow\mathbb{N}$ nondecreasing with $$\frac{g(n)}{f(n)}\rightarrow0,$$ we have $$\frac{f(n-g(n))}{f(n)}\rightarrow1.$$ So it seems like any f which is bounded linearly has this property, but I'm struggling to find a sufficient condition. Does anyone know of a simpler way of expressing this condition?
2026-04-28 13:52:25.1777384345
Equivalent conditions for $f(n-o(f(n)))\sim f(n)$
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