Real analysis Definition and 524 Threads

Coming up with counterexamples is hard. So to prove or not to prove, that depends if there exists a counterexample. Question 1 has been ANSWERED!: If f has a bounded variation on [a,b] , then is it true that f is of Riemann integration on [a,b]? Question 2 has been ANSWERED!: Is it...

Hello! I am thirteen and self studying real analysis... I'm wondering where to go after this; kinda looking for a general outline of what to do from here on out. Any help is greatly appreciated. Thank you.

So I have an exam in Real Analysis I coming up next week and I was hoping if someone can help me out. I hope my question makes sense because I think I might be confused with defining the metric space or so... Homework Statement a)Suppose that we have a metric space M with the...

Can anyone give me any help on how to get started, or how to do this problem? --- Prove that if the terms of a sequence decrease monotonically (a_1)>= (a_2)>= ... and converge to 0 then the series [sum](a_k) converges iff the associated dyadic series (a_1)+2(a_2)+4(a_4)+8(a_8)+... =...

I know that AP Calculus BC is very watered down in comparison to a real analysis course at the college level. I'm taking high school Calc I, II this upcoming school year as a junior and would like to get a good book to learn real analysis from. I'm currently looking at getting Spivak's CALCULUS...

I'm planning to learn real analysis in the up and coming holidays, anybody have any good suggestions on which textbooks will be useful? I've heard good comments about Baby Rudin, is this true?

Okay, I am a junior undergraduate in CS & Mathematics and I want to be prepared for these two classes when I take them. I am currently signed up in the fall for Real Analysis I and Modern Algebra I (among other classes). I have a strong background in Calculus, but don't have much of a...

Please help me with this one: Suppose f is a continuous real valued function on R - real #s and that 0<f(x)<3 for every x in R. Let F(x) = integral from 0 to x of f(t) dt. a) Show that F is uniformly continuous on R b) Suppose the continuity assumption is left out, but the function f is...

Consider the series 1+ Σ((1/(2^k))coskx + (1/(2^k))sinkx) (a) Show that series converges for each x in R. (b) Call the sum of the series f(x) and show that f is continuous on R = real numbers My thoughts: From trig => cos + sin = 1. So, is it something like |coskx + sinkx| / |2^k| < or =...

Suppose f: R->R is continuous on all of R and B is bounded subset of R. a) show cl(B) is bounded set b) show image set f(B) must be bounded subset of R c) suppose g:B->R is defined & continuous on B but not necessarily on all of R - real #s, Must g(B) be bounded subset of R? (Prove or give...

Hello friends, I wish to seek your assistance in helping me solve these problems regarding Real Analysis from Rudin's Real and Complex Analysis book. All problems are from the first chapter on Abstract Integration. While, I don't expect complete solutions, I hope you guys could give me some...

I'm doing this problem in the book - their are 2 of this kind and they have no answers in the back.. so i thought ill post one. Let S be the Cartesian coodinate plane R x R and define a relation R on S by (a,b)R(c,d) iff a+d=b+c. Verify that R is an equivalence relation and describe the...

Let A and B be subsets if a universal set U. Prove the following. a) A\B = (U\B)\(U\A) To do this, show it both ways. 1) A\B contains (U\B)\(U\A) 2) (U\B)\(U\A) contains A\B I'll start with 2) if x is in (U\B)\(U\A), then x is in (U\B) and x is NOT in (U\A). then (x is in U and x...

Prove: For every real number x>1, there exists two distinct positive real numbers y and z such that x = (y^2 +9)/(6y) = (z^2 +9)/(6z) Okay.. this has real got me beat. Firstly (this sounds stupid and obvious), when they give us a proof, is it really true? Do we just naturally believe...

Hey, university started and in less than a week, we allready have to hand in an assignemnt. I did most questions, i was just wondering if somebody can help check some of work - its more english than math :mad: Q1) True or False - A statement and its negation may both be false. A1) False -...

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...