Equicontinuous sequences of functions vs. continuous functions

  • Thread starter jdinatale
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  • #1
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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

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #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].
 
  • #3
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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].
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.
 
  • #4
Dick
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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.
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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