Recent content by LauraLovies

There is a theorem that states that if the functions are continuous and the sequences converge then there is uniform convergence. I just have no idea if the sequences converge uniformly or not.

Are you talking about something Cauchy?

Homework Statement For each of the following sequences (fn), find the function f such that fn --> f. Also state whether the convergence is uniform or not and give a reason for your answer. Homework Equations a.) fn(x) = 1/xn for x greater than or equal to 1 b.) f[SUB]n[SUB](x) =...

f and g are both continuous so i know that there exists some \epsilon > 0 and greater than zero that fulfills the continuity definition. It just seems to obvious to me that i don't even know where to start. \delta

I am having a lot of difficulty on my continuity problems for my Analysis class. 1. Prove that (f O g)(x) = f(g(x)) is continuous at any point p in R in three ways a.) Using the episolon delta definition of continuity, b.) using the sequence definition of continuity, and c.) using the open...

yes i know...but am i on the right track. i just can't seem to pinpoint whether the set is open or closed. and if i knew that...then i would be fine...

Homework Statement The set S = [0,1] U {3} Homework Equations I need to say whether it is closed, open, compact, complete or connected. If it is not compact, give an example why. Same thing for completeness. If its not connected, state why not. The Attempt at a Solution I think it...

im not really sure...maybe the complement of the set?

i am sure there are other points outside of the set which are limit points for sequences in the set

to any point within the set?

any suggestions? a limit or cluster point is where a sequence converges...would it converge to 1 or the whole set?

Homework Statement Find the closure, interior, boundary and limit points of the set [0,1) Homework Equations The Attempt at a Solution I think that the closure is [0,1]. I believe the interior is (0,1) and the boundary are the points 0 and 1. I think the limit point may also be...