# Equicontinuous sequences of functions vs. continuous functions

1. Jan 10, 2012

### 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

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

2. Relevant equations

3. The attempt at a solution

2. Jan 10, 2012

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

3. Jan 10, 2012

### jdinatale

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. Jan 10, 2012

### Dick

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.