Recent content by ColdCoffee

  1. C

    Proofing Change of Variable Formula for Integration

    I like the principle of what you are doing (IE, using the fact that the measure of a subset of reals is invariant under under "linear" shifts). I would check your shift again again(it looks like you shifted by h twice). Also, make sure that it is clear in the context of your class that those...
  2. C

    Does the Convergence of \(\Sigma \frac{f(x)}{x}\) Depend on \(\Sigma f(x) = 0\)?

    Ok well I wrote up a reply and then PF timed me out- so that reply went bye bye. In a nutshell- 1) I apologize if I misunderstood your argument, in hindsight I had no good reason to assume that you were using absolute convergence. 2) I am convinced that if argued carefully, your approach...
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    Does the Convergence of \(\Sigma \frac{f(x)}{x}\) Depend on \(\Sigma f(x) = 0\)?

    Its been a while since I took analysis but I would be careful with this approach. It seems to me that you are trying to use two ideas here. First, is the convergence of a series (seen as a sequence) to conclude that the sum of the limits is the limit of the sums, in this case we do not have...
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    Proofing Change of Variable Formula for Integration

    I would have to think about it a little more, but my gut instinct is that just using the strait definition of the integral(I assume this is the Riemann integral right?) would be the most strait forward approach since you are just talking about a "linear" translation on the domain. I don't think...
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    What is the countable basis problem in topology?

    Which book is this coming from? If I have it I will take a look at the chapter tonight. This problem is interesting.
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