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seen Mar 22 '13 at 1:06

Mar
21
revised Set of Continuous Functions, Functionals, and Equicontinuity
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Mar
21
comment Set of Continuous Functions, Functionals, and Equicontinuity
Wouldnt n need to be >=2 to stay within [0,1]? So then the piece is just a segment connecting -1 and 1? I'm sorry for all the questions; if this is correct I will fully understand the proof.
Mar
21
awarded  Commentator
Mar
21
comment Set of Continuous Functions, Functionals, and Equicontinuity
Last question: The affine piece connecting the two portions will just have length 2/n and will vary with n?
Mar
21
comment Set of Continuous Functions, Functionals, and Equicontinuity
Thank you very much I understand now; I was thinking of the := operation incorrectly. I appreciate your patience
Mar
21
comment Set of Continuous Functions, Functionals, and Equicontinuity
So since we have defined fn legally, as per the specified conditions on f, Fn must be in P since we define it by fn? Sorry for the repeated questions; I just want to make sure I completely understand this point.
Mar
21
comment Set of Continuous Functions, Functionals, and Equicontinuity
I see so this means that for any n, we can express Fn(x) as the integral from 0 to x of fn, meaning its in P by definition?
Mar
21
comment Set of Continuous Functions, Functionals, and Equicontinuity
Sorry for the basic question but what does := mean?
Mar
21
comment Set of Continuous Functions, Functionals, and Equicontinuity
Sorry I'm still having a bit of trouble understanding your solution. I don't quite get the justification for how the fn you constructed is an element of P. Also, is the idea that the function F it converges to is not differentiable at 1/2? Thank you.
Mar
21
comment Set of Continuous Functions, Functionals, and Equicontinuity
Thank you for your explanation. I actually had something similar for part 2 and your solution makes a lot of sense. I am still having a bit of trouble understanding part 1). How do you show that Fn is uniformly cauchy?
Mar
21
revised Set of Continuous Functions, Functionals, and Equicontinuity
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Mar
21
revised Set of Continuous Functions, Functionals, and Equicontinuity
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Mar
21
revised Set of Continuous Functions, Functionals, and Equicontinuity
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Mar
21
revised Set of Continuous Functions, Functionals, and Equicontinuity
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Mar
21
revised Set of Continuous Functions, Functionals, and Equicontinuity
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Mar
21
revised Set of Continuous Functions, Functionals, and Equicontinuity
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Mar
21
revised Set of Continuous Functions, Functionals, and Equicontinuity
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Mar
21
comment Set of Continuous Functions, Functionals, and Equicontinuity
I see how we could have a sequence fn that is differentiable on an interval and converges uniformly to f, where say f'(0) does not exist. What you are saying definitely makes sense. I am still not quite sure how to turn this intuition into a formal proof. Thank you
Mar
21
revised Set of Continuous Functions, Functionals, and Equicontinuity
edited title
Mar
20
revised Set of Continuous Functions, Functionals, and Equicontinuity
edited title