Let $f$ be a real function defined on $[1, +\infty)$ and convex from a number on.
Is it true that the sequence $f_n:=f(n)$ is unbounded?
2026-04-28 18:52:24.1777402344
Unbounded convex real functions
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The answer is no. Indeed, choose a constant function $f(x)=1$ for all $x\in[1,+\infty]$. It is convex and bounded.