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Equicontinuous sequences of functions vs. continuous functions

  1. Jan 10, 2012 #1
    Hello,

    below I have the problem and solution typed in Latex. For the first part, I just want someone to verify if I am correct.

    For the second part, I need guidance in the right direction

    math1.png
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 10, 2012 #2

    Dick

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    I think you've got the right idea for a), but your description is a little muddled. Like what is the k subscript on your delta supposed to mean? For b) think about how you would go about choosing a delta to satisfy [itex]|g_n(1)-g_n(x)|<\frac{1}{2}[/itex].
     
  4. Jan 10, 2012 #3
    Thank you. The k on the delta is just to show that for a given f_n and epsilon, you will get a particular delta which I call delta subscript k. I guess I could remove that.
     
  5. Jan 10, 2012 #4

    Dick

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    Wouldn't it make more sense that if delta depends on f_n, that that particular delta should be labeled delta_n, instead of the meaningless subscript k? That's what I'm talking about with notation.
     
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