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Sep 26, 2021 at 23:41 comment added Iosif Pinelis @CharlesPehlivanian : Perhaps one can modify/smooth out the $f$ in this example to make it continuous, while preserving the other properties. However, at this point I don't have a clear idea how to do that. You might want to ask the "continuous" version of your question separately.
Sep 26, 2021 at 23:22 vote accept Charles Pehlivanian
Sep 26, 2021 at 23:22 comment added Charles Pehlivanian Agree. Thanks. What happens if I also require $f$ to be continuous?
Sep 26, 2021 at 21:48 history edited Iosif Pinelis CC BY-SA 4.0
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Sep 26, 2021 at 20:46 history edited Iosif Pinelis CC BY-SA 4.0
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Sep 26, 2021 at 20:37 history edited Iosif Pinelis CC BY-SA 4.0
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Sep 26, 2021 at 20:16 history answered Iosif Pinelis CC BY-SA 4.0