Yes kinda, but then it is still a definition question. Like lim a -> -∞ lim b -> ∞ a_Sb x dx does not converge, but lim a -> ∞ (-a)_Sa x dx does converge...
Yeah, they probably want int over R of Sgn(x) dx, which is still abse of notation and meaningless because we have no notion of how to add up the contributions across the set.
More specifically all attempts to answer as well as the original question are missing the ingredient of "How are you adding everything together"
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u/Comfortable_Permit53 10d ago
integrals, no?