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Mar 30, 2021 at 12:51 comment added Vladimir Dotsenko @klaus I see what you meant. For some reason, the wording you use (while being correct) created the wrong quantifiers in my head, as Jens Reinhold remarks.
Mar 30, 2021 at 11:24 vote accept klaus
Mar 30, 2021 at 11:00 answer added Jens Reinhold timeline score: 1
Mar 30, 2021 at 11:00 comment added Jens Reinhold I think the misconception is that the OP wanted to allow that $f,g$ depend on the choice of $I$, but V.D. assumed the same functions should provide an example for all choices?
Mar 30, 2021 at 10:40 comment added klaus @VladimirDotsenko I'm not sure I understand you correctly. A priori there is $2^n-1$ subsets you should check this on but it is enough to check on $n$ subsets (each omitting one index). Is that what you meant?
Mar 30, 2021 at 10:18 comment added Vladimir Dotsenko If it is true for each one-element subset, then it is true for the whole set, since the action on the direct sum is the direct sum of actions, no?
Mar 30, 2021 at 10:01 history asked klaus CC BY-SA 4.0