Recent content by Kuzu

I'm taking this course "abstract algebra" at university and I've been given some homework questions. I was able to solve all of them but one. And it would be great if anyone could help me with this. The question is like this: "If all cyclic subgroups of G are normal, then show that all...

Thanks to both of you!

Hey thanks for the advice! I used partial fractions like this: \frac{A}{x+2}+\frac{B}{x-6}+\frac{B}{(x-6)^2} I found A=1/64, B=189/192 and C=49/8 some strange numbers.. is this right?

I tried to substitute x=u+2 but that didn't make it easier. Still too much work with the derivatives. \frac{x2+2x+1}{(x-6)2(x+2)} similarly I have two other questions like this, which are past years exam questions. "Find the taylor series of f(x) = \frac{x2+2x+1}{(x-2)(x+8)} at x=-3"...

I have a homework question like this. "Find the taylor series of the function f(x) = (x2+2x+1)/(x-6)2(x+2) at x=2" I'm trying to simplify this expression so I can take the derivative. I only got this far: (x+1)(x+1)/(x-6)(x-6)(x+2) Can this be simplified more so that I can easily...

\infty<-- Don't bother this, latex issue... Hey! I just returned from the exam.. and it was really good! :approve: There were two questions almost the same as Q3 with little change x2<=1000000, so the set is [-1000,1000] and everything else the same. Q4 with addition to show Boundery...

Oh sorry, I thought subset and subspace were the same. Thanks So [0,1] is subspace of [0,1]x[0,1] right? This looks hard in 2D, can't I just prove [0,1] with Cantor's Diagonal and then show [0,1]x[0,1] can't be countable either? By showing injection and cardinality.. About...

Thanks and hi, Yesterday I studied further topics and learned some new theorems in real analysis.. still trying to digest all the new definitions like compactness, open subcovers, boundedness.. :shy: I tried to solve questions 3 and 5, but I'm not really sure if its all correct and I have...

Ok thanks I'll do that, you are an angel :) Hmm, for 1000 limit points something like this maybe? I'm not sure.. is there another way? [SIZE="4"] [SIZE="1"]999 U{m+1/n|neN} [SIZE="1"]m=0 do I have to add union {0} also? I'm so new to all this :frown:, and my exam is on...

:rolleyes: Micro thanks so much! We didn't cover Cantor-Berstein but I think I get the idea.. I will consult my teacher about this method and if I can use it. btw is it ok to say that [0,1] has same cardinality as the whole set [0,1]x[0,1]? Thanks to you too JonF, But can't I just say...

I found something called Cantor's Diagonal Argument. If I say [0,1] subset of R is countable and make a list and then construct a new number with cantor's argument to prove [0,1] is uncountable, can I then say [0,1]x[0,1] subset of R^2 is also uncountable? Is this a correct solution?

Yes we have seen that R is uncountable and finite. And N is countable and infinite. I'm trying to make sense of all this. Thanks to you I think I got the idea a little now. Ok so I will not think of it as counting infinitely many elements but being able to pinpoint the next element in the set...

Hey thank you, I made some progess with a few questions but I still have big problems with some of them. For example with question 2. I guess to show that it is not countable, I have to suppose it is countable and arrive at a contradiction. For a set to be countable there should be a way for...

Oh sorry, thanks for being honest about my post, you are so right about that. I realize how rude it seems but I'm really desperate about these questions and couldn't make much progress solving them. I'm working on them... will post here about everything I come up. I thought maybe someone could...

Real Analysis Exam Questions. Please Help! I'm taking this course on real analysis and my exam will be in less than a week from now :eek: These are exam questions from previous year which have been assigned as homework, and I just started studying and it's really hard. I would be sooo happy if...