I came back to these two exercises because I really didn't understand the entire C-infinity thing along with C-0 and C-1 classes of derivation. I realize that C-0 just means said function is continuous, and C-1 must mean its derivative is continous... however I am having tremendous trouble understanding the solutions given for these two exercises on the forums. Can anyone explain them to me? That would help me the most! Thanks!

03 Jul 2009, 19:28

vasco

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Joined: 07 Jun 2008, 08:21 Posts: 235

Re: Exercise [06.04] and [06.02]

Hi Skynt I have looked at both solutions and I don't think either of them is a really satisfactory proof.

The first solution for 6.2 is very obscure and not really very illuminating. It does not relate well to Penrose's discussion of continuity and differentiability in his book. I think a more intuitive approach is needed. The second so-called solution to 6.2 does not provide any detail and so again is not satisfactory.

The solution for 6.4 seems to me to be on the right track but does not provide enough detail.

These are only my personal opinions of course.

I will try to provide more satisfactory proofs in a few days time. I just need some time to work out the details and then I'll publish them here and you and anyone else can make comments/ask questions.