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Nov 5, 2022 at 12:20 vote accept Doriano Brogioli
Nov 5, 2022 at 12:20 comment added Doriano Brogioli I tried to formalize a weaker version of the proposition, here: mathoverflow.net/questions/433954/… . If I am not wrong, it includes your example, but is still difficult to prove or dis-prove for me.
Nov 5, 2022 at 1:05 comment added Fedor Pakhomov @DorianoBrogioli I don't know, this is a really vague question. And I am not really sure what you would consider to be an improvement of the example.
Nov 4, 2022 at 22:40 comment added Doriano Brogioli I think it is correct: it proves that Prop. 1 is false. It is very ingenious, but maybe too much ad-hoc: I have the feeling that Prop. 1 could be slightly corrected to include this counter-example. It's just a feeling, due to the fact that there is a single "hard task", calculate $h^n$ for large $n$, that is carried on step-by-step by both $f$ and $g$. Suggestions to modify Prop. 1, or further counter-examples, are welcome.
Nov 4, 2022 at 14:47 history edited Fedor Pakhomov CC BY-SA 4.0
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Nov 4, 2022 at 14:37 history edited Fedor Pakhomov CC BY-SA 4.0
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Nov 4, 2022 at 14:32 history answered Fedor Pakhomov CC BY-SA 4.0