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Jun 20, 2021 at 2:20 vote accept Beta
Jun 20, 2021 at 2:20
Jun 19, 2021 at 12:11 history edited Salvo Tringali CC BY-SA 4.0
just realized that the "α/f(α)" case is essentially the same as the "αf(α)" case
Jun 19, 2021 at 10:18 comment added Beta Ok, Tringali, after your helpful examples I now clarify the statement of the question. Please forgive my fault.
Jun 19, 2021 at 9:57 comment added Salvo Tringali I think this is not a question particularly suited to MathOverflow. In any case, there you have your answer. Also, I don't think it was a good idea to add in the "α−f(α)" case: It sheds a bad light on the OP, as it's a trivial variant of the "α+f(α)" case.
Jun 19, 2021 at 9:55 history edited Salvo Tringali CC BY-SA 4.0
the OP has added in a new question and this made "first", "second", and "third" meaningless
Jun 19, 2021 at 9:46 history edited Salvo Tringali CC BY-SA 4.0
addressed the question in the 1st comment under this answer
Jun 19, 2021 at 9:40 history edited Salvo Tringali CC BY-SA 4.0
addressed the question in the 1st comment under this answer
Jun 19, 2021 at 9:32 comment added Beta @Tringali, thanks so much! I edit the question for real $f(x)$ because I realize I'm dealing with real functions. So how do you think the real case? Or is there any reference on this?
Jun 19, 2021 at 9:14 history answered Salvo Tringali CC BY-SA 4.0