Recent content by brickcitie

Homework Statement I'm asked to show that an epsilon-disc in R^n is path-connected. Homework Equations The Attempt at a Solution I can kind of understand in my head why it must be, but I literally have no clue how to begin a rigorous attempt at this. I know I need to define a...

Hi again micromass. So I mis-typed this originally; I meant to say that I need to decide whether it is guaranteed to be closed. The first part of the question was whether it was open or not, and I used the same function you just mentioned to answer that. And also, won't any infinite union of...

Quick Analysis Problem -- Related to properties of cont functions Homework Statement This problem assumes that f: R ----> R is continuous on all of R. I need to determine if the following set is guaranteed to be closed, regardless of f(x). A = {x in R | 0 <= f(x) <= 1} Homework...

AHA! I do know that a set that is not closed is not necessarily open, yet I seem to always get carried away during proofs and forget that. I understand where you were leading me now. A very clever proof. Thanks so much for your time and patience micro, you help is duly appreciated.

Ok the closure of a bounded set is closed and bounded, and since I'm dealing with R then it is compact. I know that when dealing with a continuous function the image of a compact set is always compact. But that doesn't help if the set is open and bounded. This proof basically boils down to...

Ok so then in that case I've been spinning my wheels trying to come up with a counter-example. Any tips on how to begin the proof?

I'm not quite sure how that helps though. How can I use that information to find a bounded set whose image is not bounded?

Homework Statement Ok so I'm given that we have some function from R to R, that is continuous on all of R. I am asked if it is possible to find some BOUNDED subset of R such that the image of the set is not bounded. The professor gave the hint: look at closures. Homework Equations...

Ok I think I see what you mean here. So I need to find a bound for an expression that is easier to solve for n, but is greater than my expression. Gonna attempt to solve with this method. This freaking problem sucks.

I know somebody can help me with this. I'm completely stuck.

Ok so I have made some slight progress I think, but I am unsure whether this is correct. Here is what I did: Divided both top and bottom by n^2. Numerator is -3 + (1/n) + (2/n^2). Denominator is 3 - (1/n^2). Went on to try and prove these using dfn of lim. Started with numerator because there...

Ok awesome thanks for the help Shredder. I will hit the paper with this info and see if I can progress. Will post my progress soon.

Yeah, I was able to find the limit of the numerator and denominator, and thus the limit of the entire expression, which is -1. I have no problem computing the limit, I am just having trouble proving that -1 is the limit using the definition of a limit, or the epsilon delta method.

I did that but and that's how I found that the limit is -1, but I'm still unable to complete the proof.

Homework Statement Find the following limit and prove your results using the definition of the limit: Lim (-3n^2 + n + 2)/(3n^2 -1) Homework Equations The Attempt at a Solution I passed the limit operator (if it is an operator) through and used it's properties to find that...