Real analysis Definition and 509 Threads

1.) Suppose f:[a,b]->R and g:[a,b]->R are continuous such that f(a)<=g(a) and f(b)=>g(b). Prove that f(c)=g(c) for some c in [a,b]. I started out by using the Intermediate Value Property for some c1 and c2 with f(c1)=L1 and g(c2)=L2. I am trying to conclude that L1=L2. This was one approach...

Hey guys. I was just wondering how your first experiences with real analysis was, such as "how it was taught," "how the exams were like," etc. I thought it was relatively easy since the lectures emphasized the proofs of theorems and a sufficient amount of examples. The exams were to prove...

Well, this semester I'm in my first directed study in real analysis. I'm on my own. sort of worried about doing it, just got the book, and it looks kinda tough. I'm going to have to rethink how i go about classwork. i won't be rushing to get anything done before it's due or anything like...

I'm a physics major (undergrad) who wants to learn real and complex analysis, but don't have the time to do the courses in my programme. Can anyone recommend a good textbook for learning the subjects on your own?

We must find the accumulation point for the set E = \left\{ \frac{n^2 + 3n + 5}{n^2 + 2} \vert n \in \mathbb{N} \right\} Now that is easy, we first rearange the terms so we see what happens in this mess when n varies. I did the following thing.. E = \left\{ \frac{n^2 + 2 + 3n + 3}{n^2...

Show that the intervals (0,1) and [0,1] are equivalent. (Hint: consider rationals and irrationals separately). I'm able to find a function that shows a bijection between (0,1) an [0,1] under the irrationals, but i can't figure out the rationals. Also... the next step (i believe) would be to...

Show that the intervals (0,1) and [0,1] are equivalent. (Hint: consider rationals and irrationals separately). I'm able to find a function that shows a bijection between (0,1) an [0,1] under the irrationals, but i can't figure out the rationals. Also... the next step (i believe) would be to...

I know that this board will be really good...but I was wondering in terms of something to supplement my textbook... do you guys know any sites w/ explanations and lectures, so I can understand teh topic better?

Has anyone ever seen this? It's an interactive online textbook in analysis in a single real variable. As an undergrad, I wussed out and took Advanced Calculus instead of Analysis, and this is a subject I've been meaning to learn. Is anyone interested in going through this...