Recent content by bw0young0math

Thank you so much!Thank you!

Thank you for your reply.:D Um.. I have a question. If interval B=(a,b)(b=∞), length of B is infinite. Then how can I prove this?(Because I cannot define an half of the length B when length of B is infinite.) & How did you think of an half of length of B? I wonder the inference.

Hello, I have a problem. I think this problem about 5 hours. But I couldn't finish this. In fact, I solve a little. But I don't know whether it is right or not. If you check this problem, I really appreciate you.. *This is the problem from Bartle 5.1 #14. Let $A=(0,∞)$, $k:A→\Bbb R$ is given...

Hello, today I have a question. If uni.cont. function sequence fn on (0,1) is uni.conv. to f on (0,1), then f is uni.cont. on (0,1). The above is true. The wonder I have is...May I prove the above by this way? This way: fn is uniform continuous on (0,1). So Fn is continuous on [0,1] (by...

Thanks! I understand it! F(a)and F(b) are isomorphic so we can think that they have the same algebraic constructure and algebraic properties. Thank you:)

Hello everyone. At first, I appreciate your click this page. I have a book named 'A first Course in Abstract Algebra 7th' by Fraleigh. I have a question about 'relation algebraic property with conjugate' in automorhisms of fields. in page415, this book explains "Let E is algebraic extension...

Hello. At first, I want to tell you I'm so sorry because I wrote problems in detail. The problem is judging when the improper integrals are convergent. (i.e., the problem is finding the ranges for the improperintegrals: convergent.) I wrote the problems' solutions I have in my blog. (The file...

Hello. I'm studying improper integrals in real analysis. However, two problems are very difficult to me. If you are OK, please help me.(heart) 1.2. I have solutions about above problems. However, I don't know how I approach and find the way for solving them.

Re: Ambiguity in the Arc Tangent Function At first, thanks for your help. :o I understood your meaning that they have same values consequently. Right? However, arctan(5/(-5)) can't express -ㅠ/4. Thus I can't understand why they are the same.Also,you mentioned about x, y, and quadrant. My...

This problem is about complex analysis. Why arctan(5/-5) is different from arctan-1(-5/5)? tan-1(5/-5)=3ㅠ/4 +2kㅠ tan-1(-5/5)=-1ㅠ/4+2kㅠ (k :arbtrary integer.) Why can't I calculate just arctan(-1)?I thought that it is related withe tangent peoriod ㅠ not 2ㅠ. However I can't know that exactly...

Hello. Today I study domains but I have some problems. Please help me. I learned Z[root(-3)] is not UFD. Then Z[root(-3)] is a example about gcd-domain( there exist some elts a,b in domain D such that it does not exist gcd(a,b).) Let a=2, b-1+root(-3) . a and b are not associates and they...

Hello. I have some problems with proving this. It is difficult for me. Please help me.:confused: "For arbitrary irrational number a>0, let A={n+ma｜n,m are integer.} Show that set A is dense in R(real number)

Hello. I'm using phone now. So I can't write in detail. Sorry. You can convince them with "Principle of mathematical Induction. " If you have a book "introduction to real analysis" from Bartle, please see p.12-13. I'm so sorry not to write here in detail. Please click. I uploaded about the...

Thanks! I discussed this problem with my friends today. Including your explanation and my all opinion about this problem, I told them. Also, I really understand and accept all about this problem. I really appreciate you.:o

I understood you meant "there must exist some sequence $y_n\to0$ such that $f(y_n)$ does not converge to $L$ "in my second part does not need to be "there exist some sequence $y_n\to0$ such that $f(y_n)$ does not converge to $M$ ≠ $L$ So my proof needs to add about M. Do I understand your...