Equicontinuous sequences of functions vs. continuous functions

[jdinatale]

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

 

[Dick]

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 $|g_n(1)-g_n(x)|<\frac{1}{2}$.

 

[jdinatale]

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 $|g_n(1)-g_n(x)|<\frac{1}{2}$.

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.

 

[Dick]

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.