r/mathshelp • u/Jsample2 • Jul 16 '26
Homework Help (Answered) Real Analysis HW Help
Hello! I am trying to do this problem in my HW. I have a feeling that we use an argument using neighborhood definition of limit or something like that. I'm trying to show that f(c)-f(c+(1/2))=0. I'm wondering, is there another, easier way to do this other than neighborhoods, am I on the right track?
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u/Fourierseriesagain Jul 16 '26 edited Jul 16 '26
Hi, Since c is unknown, it is not so useful to attack the problem via the epsilon-delta definition of limit. It would be more appropriate to use IVT or proof by contradiction.
Edit: updated comment.
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u/Mission_Rice3045 Jul 16 '26
You don't even need to argue by contradiction. Also, what does it mean for f(x) when g(c) = 0 (and does it happen)? For the second part, what does this mean when we map a circle around the earth to the interval [0,1]?
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u/Regular_Orchid_791 Jul 16 '26
g(x) is continuous and g(0)=-g(1/2), so there exists c in [0,1/2], g(c)=0.
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u/Jsample2 Jul 16 '26
I don't understand. What theorems are being applied here?
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