Recent content by sitia

Homework Statement I have the function f(x) = x if x= 1/n and n is an integers / {0) = 1- x otherwise and the function g(x) = x if x is rational =1- x if x is irrational The problems is to...

Why is x=1 a problem point? Cant we have a equal to 0 for f(x)?

Homework Statement Hi everyone, I'm kind of struggling with determining continuity of functions.Homework Equations The Attempt at a Solution For example, f(x)=|x-1| I know is continuous on ℝ but how do I show this clearly. I my head, I just think that the function is valid for any value of x...

You are right, I have the definition but that's when I'm struggling...truly understanding it and applying it.

I struggle with how/what process I need to follow to find accumulation pts of a set or determining of a given value is an accumulation pt.

Homework Statement Hi guys, I'm having real difficulty with understanding accumulation points. I don' really know why that is since others seem to understand the concept fine but I'm very lost. For example, I'm practicing some questions and one of the is : If S is the set of rational...

Oh wow, stupid mistake. Thanks! So, do I need to show anything to show divergence or just state that it's going to zero and infinity..oscillating, so it's divergent?

Isn't it 1/(2^2)^2

I have...1/4, 1/16...etc

Homework Statement For the sequnce an defined recursively, I have to determine the limiting value, provided that it exists. a1=2 and a(n+1) = 1/(an)^2 for all n Homework Equations The Attempt at a Solution Ok, so I 've done problems like this but the a(n+1) was biggger than...

How do you find an upper bound? Sorry I' m a little new to this and confused

Yeah but for this case, I have to have a lower bound

Is that all you do to determine lower boundness? Check is numerator and denom are positive for all n>0 ? So for a sequence such as n/2^n which is decreasing, you determing lower boundness becasue both n and 2^n are positive for all n>0?

How do you determine boundeness by comparing the fraction to 1. upper bound, lower bound, etc?

What does knowing which is bigger in the original problem show about boundness? So the denom being bigger in this case means what? Thanks for all the help btw!