Recent content by Pen_to_Paper

ok, here is my problem, i know the delta-epsilon proof for continuity; f is continuous at every point p if there exists an epsilon>0 such that delta>0 and I don't know the logic principles well enough to construct a way to disprove it. Is it: for every epsilon there exists a delta>0 such that...

As long as you got it to RREF, then you can see if there is a pivot in each column, if there is, then these vectors span R4. If there is not a pivot in each, then they do not span R4. Good luck!

Do you know how to set up these four vectors as columns to make a 4x4 matrix? Have you done row reducing? Because that would also be an approach to determining if they are linearly independent.

Oops! I mean to say the original problem is this:

"I'm not sure why you want to take G the set of all discontinuities. I can't see how that helps. Secondly, if you take G the set of discontinuities, then G is not necessairily open... " I want to take G (the set of discontinuities) because I thought I was using G, namely f(G), for the diam...

Because if you've worked with the adjoint of a matrix (or if you haven't yet) an equation for A-1 (A inverse) = 1/det(A) * Adjoint (A) here, don't worry about what the adjoint is, you may or may not work it out in your class; but you can see how from this formula, if det(A) = 0, then A...

micromass, thank you for the quick reply, but I'm not sure what the y and f(y) are in the diam f(G) equation is it a way of saying f(x)=y ( the function going from metric space X to Y) ? but then, what is f(y)? Separately, if G is the set of all x discontinuous on f, then isn't f(G)...

My advice to you is to set up vectors u,v as a 2x2 matrix and plug in values for t; then how do you conclude that a matrix has linearly independent vectors?

Homework Statement X, Y are metric spaces and f: X \rightarrow Y Prove that f is discontinuous at a point x \in X if and only if there is a positive integer n such that diam f(G) \geq 1/n for every open set G that contains x Homework Equations diameter of a set = sup{d(x,y): x,y...

Thank you! I found this part in particular very, very helpful: "Yes, a subcover is just a subset of the cover such that this subset still covers the entire space. For example, {(0,1),(1/2,2),(1/2,3/2)} will be an open cover of (0,2). A subcover would be {(0,1),(1/2,2)}. A subcover would NOT...

First off, I'm using Rudin in my Analysis class, and although I have the written definition of a cover, I don't quite grasp it: "An open cover of a set E in a metric space X is a collection of {G sub-alpha} (G indexed by alpha's) of open subsets of X such that E is contained in the union of the...