Recent content by varygoode

Wait, why are we talking about [0,1]? Damn, I'm completely lost here. Can you give me this explanation in some mathematically explicit terms? I'm having trouble following what's going on here.

It's uniformly continuous since it is continuous on a compact set, right? So for every epsilon > 0 there exists delta > 0 s.t. |x-y|< delta implies |f(x) - f(y)| < epsilon. I've got that I think. But I need something else to connect that and the rectangles. I'm horrible at picturing...

I think I can easily find countably many rectangles to cover the diagonal you are talking about. Something like if I take all the intervals on the line, all of length 1 let's say, then I can cover the interval by n squares with height epsilon/n. Then if I take the union of them, I'll get the...

Homework Statement Homework Equations The Attempt at a Solution I'm pretty clueless as to what's going on here. If someone can just please lead me in the right direction, I would be quite grateful.

Alright, I think I understand what's going on with f. So then with g, couldn't I try a similar idea since it is also absolute value? Or no?

When they're ALL zero? Because if one x_i is non-zero, but the rest are, it's still differentiable? I don't know why or how to prove it though, and that's what I need help with.

Everywhere except at x=0.

Homework Statement Homework Equations The Attempt at a Solution I think to determine where it's differentiable it has something to do with partial derivatives. But I am just so completely clueless on how to even start this guy off that any tips or minor suggestions on where to...

Thanks so much EnumaElish, this problem is solved.

Use it where? Are you responding to my response to you or my response to Ivy? (Or both?)

I'm not exactly sure where you got the value for f(1) since I never gave f(x) a definition, but I'll go with you on it. Hmm... here's what I'm thinking now: If x \in \bar{A}, \ \ \exists some sequence (x_k) \in A s.t. \lim_{\substack{k \rightarrow \infty}} (x_k) = x . Then f(x) =...

[SOLVED] Uniform Continuity Homework Statement Let A \subset \mathbb{R}^n and let f: A \mapsto \mathbb{R}^m be uniformly continuous. Show that there exists a unique continuous function g: \bar{A} \mapsto \mathbb{R}^m such that g(x)=f(x) \ \forall \ x \in A . Homework Equations...

If your answer is: -2 + c Then no, not even in the ballpark. Please explain what you did to arrive there. Note "antiderivative" is the same as "indefinite integral". To check your answer, take the derivative. If you arrive at the question, you have the right answer. (Unless of...

I was saying if it makes sense, it has a proof. So if you can't come up with a solid proof, there's a higher chance it doesn't make sense. But see, in your second "definition" you talk about the closure of a set A. But the closure is defined as the set A unioned with the set of all of A's...

If you're right, you'll be able to prove it. You're just making everything exponentially more complicated than it actually is. True mathematicians aim for simplicity.