Let $f:]a,b[\to ]a,b[$ an involution not necessarily continuous . It's true that $$\lim_{x\to b^-} f(x)=a\iff \lim_{x\to a^+} f(x)=b\quad ?$$ I can't find any counterexample
Addition: Question resolved
2026-04-03 12:34:06.1775219646
Limit of an involution at the extremities
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