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...