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Real Analysis Guest Book
Real Analysis Guest Book
teaching page at the
Math Dept CU-Denver.
Andrew Knyazev
lim (f(x) + g(x)) = lim f(x) + lim g(x) x->a x->a x->aexactly on what domains are the functions defined. In fact domain ( f + g ) = domain (f) intersect domain (g) and so on. All in all, I think attention should be given to when definitions are meaningful. Anyway, it was fun down at this place. Please see Ong Ming Yuan's other comment above
Mark Whitacre, Physics & Analysis Instructor, Lebanon High School, http://www.llion/~mwhitacr/phy/physics.html
This is false... becuase M is not divisible by any prime from 2..N doesn't imply that M is prime. It might be divisible by a number between (N+1)...(M-1). This still proves that N is not the biggest prime, since there is either a prime in the range (N+1) ...(M-1) that divides M or M is a prime.
I've seen this proof written so many times like this, and just bugs me sometimes... Pet peeve, I guess, Amir Shimoni After some discussions, we clarified the problem - the proof that's in the text was and is correct, and illustrates "p roof by contradiction", which often leads to confusions
I tried every imaginable method to approach this problem. I treated it as a power function and an exponential fuction. I currently have not a clue. Please, do not feel obligated to answer this question. I believe it is my extreme "end-of-the-year" stre ss syndrome that caused me to email this. Anyway, I will continue to wallow over this one. I still haven't gone through all of the web site. From what I can see know, I should be able to find the answer to this specific problem. Thank you for your time in reading this. Cordially, Ranjan A. Pillay
P.S. Did I mention that this was a very impressive site?
Su trabajo me ha representado un estmmulo para seguir cultivando las matemBticas, la tecnologma y mi sentido estitico. Felicitaciones desde Hermosillo, Sonora. Mixico.
Once again thank you for creating these pages. I am looking forward to when you get the area of "Metric Spaces" done, as General Relativity and Tensor analysis is another area I am on a personal quest to learn.
I just wanted to say how much your book has helped me these past two weeks during the introductory part of my Real Analysis class. Please keep working on this! It is just fantastic.
amity warren (friday@lungfish.com)
I believe the first term should be 1/2 and not 1, since the series starts when n is equal to one, not zero. Thus the Sum of the series should be one, and not two.Correct - has been fixed, thanks a lot ! - bgw Thank you for your time. Yours, Tim Maull
http://www.hk.super.net/~cismath/IBH.htm.
I have already mentioned "Interactive Real Analysis" (see the page on Functions and Calculus) and am now asking your permission to use some of your gif's. I am thinking particularly of incseq.gif to illustrate a monotone, increasing sequence, which could illustrate item 4.2 of the optional material on the syllabus. Any use would be fully credited and stricty for non-commercial use.
Yours truly, Paul Marshall, Head of Mathematics, Chinese International School, Hong Kong
Well, It is pleasant to find explanations that I can follow without feeling like a perfect idiot (wich was the case in somme foudational texts) I am not sure my understanding is correct, but I have the feelling of acquiring something new and useful for my further researchs.
Excuse my English, This is not my mothertongue wich is French.
It is absolutely great how you did the typesetting on this - small images are well-done, it's grand - btw, did you know that IBM released a TeX plug-in for netscape, so in theory, perhaps in the future, stuff like this will be possible to type-set in TeX and put on the web immediately. As a comment, your Java tools are absolutely amazing! Pete and I we are still wowing. Oh, it does not work in Internet Explorer 3.01, for some reason. Did you have any personal quarrels with Billy Gates? :)
Any plans for making an online textbook for complex analysis? Well.. Thanks for the great resource! P.S. Here's a suggestion, we found this missing, in your presentation of Algebra on series, it'd be really COOL to have a counterexample for the term-by-term multiplication of series: if sum(x_k) and sum(y_k) are convergent, then sum(x_k y_k) is not necessarily convergent, say for x_k=y_k=((-1)^k)/sqrt(k)... This was also missing in the textbook we're using and gave us headaches. :) Anyway, again, this is just way too cool. "It was cool." --Pete.
Janie Levine Hellyer, editor
Family Learning Exchange
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